DOSEN PROFIL LENGKAP

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct...

Look up undecidable or undecidability in Wiktionary, the free dictionary. Undecidable may refer to: Undecidable problem in computer science and mathematical...

In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not...

arbitrary formulas are included in the theory. Many important problems are undecidable, that is, it has been proven that no effective method for determining...

word undecidable, the term independent is sometimes used instead of undecidable for the "neither provable nor refutable" sense. Undecidability of a statement...

JSTOR 2371045. Reprinted in The Undecidable, p. 89ff. The first expression of "Church's Thesis". See in particular page 100 (The Undecidable) where he defines the...

run forever. Alan Turing proved in 1937 that the halting problem is undecidable, meaning that no general algorithm exists that can correctly solve the...

Sätze der Principia Mathematica und verwandter Systeme I" ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper...

in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP,...

In mathematics, a conjecture is a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or...

NP-complete, the SMT problem is typically NP-hard, and for many theories it is undecidable. Researchers study which theories or subsets of theories lead to a decidable...

accordingly. Some of the most important problems in mathematics are undecidable, e.g. the halting problem. The field of computational complexity theory...

axiomatized fragment of PA that is recursively incompletable and essentially undecidable. The background logic of Q is first-order logic with identity, denoted...

(do two given context-free grammars generate the same language?) is undecidable. Context-free grammars arise in linguistics where they are used to describe...

compressed as possible (to reduce overfitting). Planning in POMDP is undecidable in general. However, some settings have been identified to be decidable...

is consistent. A statement is independent of ZFC (sometimes phrased "undecidable in ZFC") if it can neither be proven nor disproven from the axioms of...

An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two-dimensional figure...

The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem...

The matrix mortality problem is known to be undecidable when n ≥ 3. In fact, it is already undecidable for sets of 6 matrices (or more) when n = 3, for...

of Peano arithmetic or not. Hence, PA is an example of an undecidable theory. Undecidability arises already for the existential sentences of PA, due to...

states that for all non-trivial properties of partial functions, it is undecidable whether a Turing machine computes a partial function with that property...

is undecidable since this allows encoding of the undecidable theory of integers (see Richardson's theorem). Still, one can handle the undecidable case...

the existence of undecidable statements had been known since Gödel's incompleteness theorem of 1931, previous examples of undecidable statements (such...

dominant logic used by mathematicians. In 1931, Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems, which proved...

Computing Machine Davis, Martin, ed. (2004) [1965]. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions...

surprising being that almost all axiomatic systems can generate certain undecidable statements not provable within the system. The definition of a formal...

problems in physics List of unsolved problems in mathematics List of undecidable problems List of NP-complete problems List of PSPACE-complete problems...

in all finite models. Trakhtenbrot's theorem shows that this is also undecidable. Some notations: S a t ( Φ ) {\displaystyle {\rm {{Sat}(\Phi )}}} means...

prove from T that σ is false. Sometimes, σ is said (synonymously) to be undecidable from T. (This concept is unrelated to the idea of "decidability" as in...

finitely presented semigroups. Only in 1947 was the problem shown to be undecidable— this result was obtained independently by Emil Post and A. A. Markov...

Likewise, a reduction computing a noncomputable function can reduce an undecidable problem to a decidable one. As Michael Sipser points out in Introduction...

solved. Inference in both Horn clause logic and first-order logic is undecidable, and therefore intractable. However, backward reasoning with Horn clauses...

proofs of impossibility found in the 20th century were those related to undecidability, which showed that there are problems that cannot be solved in general...

Publications, Mineola, NY, 2003. Davis, Martin, ed. (1965), The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions...

mathematical logic Decidable problem and Undecidable problem Gödel's incompleteness theorem, a theorem on the undecidability of languages consisting of "true...

theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about the program's behavior (for instance...

proving a number of mathematical theories undecidable. In 1950 Robinson proved that an essentially undecidable theory need not have an infinite number of...

problem by first showing that the halting problem for Turing machines is undecidable: it is not possible to decide algorithmically whether a Turing machine...

logical consequence of φ. Unlike propositional logic, first-order logic is undecidable (although semidecidable), provided that the language has at least one...

number. These numbers play a key role in Alan Turing's proof of the undecidability of the halting problem, and are very useful in reasoning about Turing...

instances as well. Some deep results of computational theory concern the undecidability of this question in many important cases. In computer algebra one often...

intuitionistic type theory. Gérard Huet has shown that unifiability is undecidable in a type-theoretic flavor of third-order logic, that is, there can be...

algorithmically undecidable word problem. Indeed, it is fairly easy to construct a finitely generated recursively presented group with undecidable word problem...

extended to show that deciding whether a CFG is inherently ambiguous is undecidable, by reduction to the Post correspondence problem. It can also show that...

are true or false. Many problems in mathematics have been shown to be undecidable after these initial examples were established. In 1947, Markov and Post...

general, undecidable in Turing's original paper. Rice's theorem shows that any non-trivial question about the output of a Turing machine is undecidable. A universal...

shown that the problem of determining the existence of a spectral gap is undecidable in two or more dimensions. The authors used an aperiodic tiling of quantum...

sensible and must therefore remain unknowable. Modern inquiry encompasses undecidable problems and questions such as the halting problem, which in their very...

natural number in a finite number of steps. A set is noncomputable (or undecidable) if it is not computable. A subset S {\displaystyle S} of the natural...

that a natural generalization of the Collatz problem is algorithmically undecidable. Specifically, he considered functions of the form g ( n ) = a i n +...

problems, formulated as ranging over all finitely presented groups, are undecidable. In the case of the isomorphism problem, this means that there does not...

shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems (1931), showing...

Principia Mathematica und verwandter Systeme (called in English "On Formally Undecidable Propositions of Principia Mathematica and Related Systems"). In that...

is also the first question in ordinary mathematics proved undecidable in ZFC; Undecidable even if ZFC is augmented by taking the generalized continuum...

which is undecidable for certain alternating multi-head finite automata over single-letter alphabets. The emptiness problem is undecidable for context-sensitive...

However, type inference in System F (without explicit type annotations) is undecidable. Under the Curry–Howard isomorphism, System F corresponds to second-order...

2022-01-23. Retrieved 2022-01-23. Feferman, Solomon (1998). "Deciding the undecidable: Wrestling with Hilbert's problems" (PDF). In the Light of Logic. Logic...

the partially ordered set of computably enumerable Turing degrees is undecidable. Paris, J.; Harrington, L. (1977), "A Mathematical Incompleteness in...

distinction between parsing and execution, and makes syntax analysis an undecidable problem in these languages, meaning that the parsing phase may not finish...

Verleden Tijd Florian Short film De Overkammer Archie Short film 2022 #No_Filter Tyler 2025 Undecidable (posthumous release) Arturo Reyes Short film...

whether it is homeomorphic to a given geometric object. This problem is undecidable for any d-dimensional manifolds for d ≥ 5 {\displaystyle d\geq 5} . Abstract...

on it. Philip K. Hooper proved in 1966 that the mortality problem is undecidable. This is true both for a machine with a tape infinite in both directions...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

to need more than exponential run time. Even more difficult are the undecidable problems, such as the halting problem. They cannot be completely solved...

truth of arbitrary propositions in a first-order mathematical theory, is undecidable. This is known as Church's theorem. His invention of the lambda calculus...

theorem states that certain properties of formal language classes are undecidable. It is named after the computer scientist Sheila Greibach, who first...

quintic equation algebraically. Also provably unsolvable are so-called undecidable problems, such as the halting problem for Turing machines. Some well-known...

halt. The undecidability of the halting problem (the problem of testing whether a Turing machine eventually halts) then implies the undecidability of Wang's...

can express both multiplication and addition, the resulting theory is undecidable. If we have an ordering predicate on natural numbers (less than, < {\displaystyle...

answered by computation; more technically, that some decision problems are "undecidable" in the sense that there is no single algorithm that infallibly gives...

determine whether a given program halts for a given input and which is undecidable. The termination analysis is even more difficult than the halting problem:...

{\displaystyle R} ⁠ can be of any complexity class, or it can even be an undecidable problem such as the halting problem. If another problem ⁠ R ′ {\displaystyle...

required/advisory) Third edition: 2012 (directives; rules, Decidable/Undecidable) MISRA compliance: 2016, updated 2020 MISRA C:2023 (MISRA C Third edition...

propositions are known as formally undecidable propositions. For example, the continuum hypothesis is undecidable in the Zermelo–Fraenkel set theory as...

Kurt Gödel described the representing function in his 1934 paper "On undecidable propositions of formal mathematical systems" (the symbol "¬" indicates...

undecidability. He showed that the Post correspondence problem (PCP) of satisfying their constraints is, in general, undecidable. The undecidability of...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

results showing that the classification of four-dimensional manifolds is undecidable: no general algorithm exists for distinguishing two arbitrary manifolds...

of violation of a specification on the final result of a program) is undecidable: there is no mechanical method that can always answer truthfully whether...

Publishers. pp. 137–160. Davis, Martin, ed. (1965). The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions...

arithmetic is also incomplete by Gödel's incompleteness theorem. In his 1953 Undecidable theories, Tarski et al. showed that many mathematical systems, including...

semantic properties of programs are undecidable. The theorem has the immediate consequence that it is an undecidable problem to determine if two lambda...

(termination proof) can never be fully automated, since the halting problem is undecidable. For example, successively searching through the positive integers (1...

Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about...

comes at a price when the type inferences (and other properties) become undecidable, and when more attention must be paid by the programmer to annotate code...

analysis indicates that some optimization problems are NP-complete, or even undecidable. Also, producing perfectly optimal code is not possible since optimizing...

superposition or quantum entanglement. Problems that are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms...

Stephen Cole Kleene used a third value to represent predicates that are "undecidable by [any] algorithms whether true or false" As with bivalent logic, truth...

time itself may not be predictable by a halting program, due to the undecidability of the halting problem. In response, Tegmark notes that a constructive...

Intuitionism (with respect to Brouwer). Martin Davis (ed.) (1965), The Undecidable, Raven Press, Hewlett, NY. Compilation of original papers by Gödel, Church...

always order a printing and a motion, right, left, or none" (footnote 12, Undecidable, p. 300) Like Turing, he defined erasure as printing a symbol "S0". And...

Giorgi Japaridze in 1992. Interpretability logic Tarski, Alfred (1953), Undecidable theories, Studies in Logic and the Foundations of Mathematics, Amsterdam:...

algorithmic implementations are guaranteed to terminate with an answer, or undecidable, meaning that they may never terminate. By bounding the scope of possibilities...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

formalism say. Decision problems become harder to answer or completely undecidable. Formal language theory mostly studies formalisms to describe sets of...

instead of justifying them. Skepticism – Knowledge is impossible or undecidable. Robert Fogelin claims to detect a suspicious resemblance between the...

mass gap (a special case of a spectral gap) in a system is known to be undecidable, meaning no computer algorithm exists that can find the answer programmatically...

disproved from these axioms. In this sense, the continuum hypothesis is undecidable, and it is the most widely known example of a natural statement that...

"reasonable" properties of finitely presentable groups are algorithmically undecidable. The theorem is due to Sergei Adyan (1955) and, independently, Michael...

Handbook of Proof Theory. North-Holland: 476–546. Alfred Tarski, Andrzej Mostowski, and Raphael Robinson (1953) Undecidable Theories. North-Holland. v t e...

Specifically, the algorithm cannot solve the constant problem, which is undecidable when it needs to determine whether an arbitrary complex number expression...

"poison"] actually do interpretive violence to what would otherwise remain undecidable." Whereas a straightforward view on Plato's treatment of writing (in...

if any, are not applied to enough arguments to be simplified. It is undecidable whether a general combinatory term has a normal form; whether two combinatory...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

TGDs (or more generally EDs) and, if it terminates (which is a priori undecidable), outputs an instance that does satisfy the TGDs. A tuple-generating...

programmer to alter the behavior of the parser make syntax analysis an undecidable problem, and generally blur the distinction between parsing and execution...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

polymorphic recursion is equivalent to semi-unification and therefore undecidable and requires the use of a semi-algorithm or programmer-supplied type...

that a natural generalization of the Collatz problem is algorithmically undecidable. Related to that, he developed the esoteric programming language FRACTRAN...

In mathematics, Richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, π, ln 2...

used this device to prove that even in those more powerful systems, undecidability is still present. Turing's oracle machines are mathematical abstractions...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

may therefore execute arbitrary programs. By the halting problem it is undecidable whether an arbitrary program executed in the Game of Life would ever...

problem History of the Church–Turing thesis Lambda calculus List of undecidable problems Post correspondence problem Post's theorem Primitive recursive...

Roger Hayward's Undecidable Monument...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

included in The Undecidable. The mathematics of Church, Rosser, and Kleene that appear as reprints of original papers in The Undecidable is carried further...

called non-computable or undecidable. An extension of the halting problem is called Rice's theorem, which states that it is undecidable (in general) whether...

Lakatos The Principles of Mathematics — Bertrand Russell On Formally Undecidable Propositions of Principia Mathematica and Related Systems — Kurt Gödel...

satisfiability is undecidable. More specifically, it is a co-RE-complete problem and therefore not semidecidable. This fact has to do with the undecidability of the...

This fragment is often preferred to MTL because some problems that are undecidable for MTL become decidable for MITL. A MITL formula is an MTL formula,...

THOG. For each of the other symbols, are they a) definitely a THOG, b) undecidable, or c) definitely not a THOG?" Presented in this form, the task is quite...

Hilbert-Bernays provability conditions do not obtain), one can construct formally undecidable (or even formally refutable) Henkin-sentences for the arithmetical system...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

vulnerability. Due to many forms of static analysis being computationally undecidable, the mechanisms for performing it may not always terminate with the correct...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

cannot be accepted in linear time in the general case. Furthermore, it is undecidable whether a given context-free language is a linear context-free language...

another result proved by Berger: that the so-called domino problem is undecidable, disproving a conjecture of Hao Wang, Berger's advisor. The result is...

conjunctive query) is known as the Datalog boundedness problem and is undecidable. Extensions of conjunctive queries capturing more expressive power include:...

United States - Japan - Europe. Contradictions of the free market. The undecidable conflicts between protectionism and free trade. The unstoppable flow...

consisting of one rule with a linear left-hand side is undecidable. Termination is also undecidable for systems using only unary function symbols; however...

Banal Reality: Comparative Thoughts on Simulation and Concreteness". The Undecidable Unconscious: A Journal of Deconstruction and Psychoanalysis. 6 (1): 29–45...

science, such as the variation of the proof that the halting problem is undecidable that uses Rice's Theorem. Due to security concerns regarding the Trusting...

problem is undecidable. 1955 - Evertt William Beth develops semantic tableaux. 1958 - William Boone independently proves the undecidability of the uniform...

that case. The satisfiability problem for monadic second-order logic is undecidable in general because this logic subsumes first-order logic. The monadic...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

The word problems for certain groups provide well-known examples of undecidable problems. If A {\displaystyle A} is a finite set of generators for G...

{\displaystyle \beta \eta } -equivalence is undecidable. Huet showed in 1973 that 3rd order unification is undecidable and this was improved upon by Baxter in...

complementation (i.e., builds the complement automaton), or can the task be undecidable? Again, the answer to this question depends on the automaton class used...

of validity in first-order logic on the class of all finite models is undecidable. In fact, the class of valid sentences over finite models is not recursively...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

multiplication. A property that is undecidable already for context-free languages or finite intersections of them, must be undecidable also for conjunctive grammars;...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

theories within the study of groups to be undecidable. Earlier, Alfred Tarski proved elementary group theory undecidable. The period of 1960-1980 was one of...

abstraction refinement, and barrier certificates. Most verification tasks are undecidable, making general verification algorithms impossible. Instead, the tools...

parameter types and covariance of the return type. Behavioural subtyping is undecidable in general: if q is the property "method for x always terminates", then...

limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like halting problems is extremely hard to detect but does not...

grammars that are not LL(k) grammars and vice versa. In fact, it is undecidable whether a given LL(1) grammar is LALR(k) for any k > 0 {\displaystyle...

found by an efficient algorithm, but for higher dimensions this is an undecidable problem. Nevertheless, computer searches have succeeded in finding these...

this poset is a lattice. The theory of this lattice is known to be an undecidable problem. Similarly, the set of all computably enumerable vector spaces...

{M}}} interprets another whose theory is undecidable, then M {\displaystyle {\mathcal {M}}} itself is undecidable. For a sequence of elements a 1 , … , a...

Neumann suggested to Gödel that he should try to transform his results for undecidable propositions about integers. Less than a month later, von Neumann communicated...

In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. The name of the subject contrasts...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

programming language theory. The equivalence of two lambda expressions is undecidable (but see unification (computer science)). This is also the case for the...

University. In 1964 he successfully defended his PhD thesis "Decidable and Undecidable Theories" (advisor Anatoly Maltsev). In 1966 he successfully defended...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

CRC Press, p. 233, ISBN 9781466513457. For more on this subject, see undecidable problem. Chomsky, Noam (Sep 1956). "Three models for the description...

"Scientism and Scientific Knowledge of Things and God", Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God, Dordrecht:...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

to handle using OOP's concept of inheritance. Behavioral subtyping is undecidable in general, so it cannot be easily implemented by a compiler. Because...

number of agents can join the system at runtime, the problem is generally undecidable, though solutions are available for specific cases. Even more so in the...

arithmetic Tarski's undefinability theorem Church-Turing theorem of undecidability Löb's theorem Löwenheim–Skolem theorem Lindström's theorem Craig's theorem...

p. 130. Kleene 1952, p. 46. Gödel, Kurt (2022) [1962]. On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Translated...

type inference algorithms, which often came out to be NP-hard, if not undecidable with respect to termination. Thus the HM performs as well as the best...

for graphs that are not constrained to be finite remains undecidable. It is also undecidable to distinguish between the first-order sentences that are...

hence it is recursively enumerable. On the other hand, the problem is undecidable. Some other recursively enumerable languages that are not recursive include:...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

have been followed. In the general case, spatial memory correctness is undecidable. If any proof of spatial memory correctness is to be made, it is therefore...

special case of superinformation. Calculating Space Computability theory Undecidable problem Quantum circuit Generalized probabilistic theory Heaven, Douglas...

syntactical incompleteness result in the introductory section of "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I". The paradox...

colors on adjacent domino edges. He observed that if this problem were undecidable, then there would have to exist an aperiodic set of Wang dominoes. At...

eye that causes the story to hover between tragedy and farce. This undecidability is the symptom of the scale of the novel's address. Wright is that rare...

formalism for real-time systems. Full MTL over infinite timed words is undecidable. The full metric temporal logic is defined similarly to linear temporal...

accessed; determining the latter requires code analysis, and is in general undecidable. Syntactic garbage is a (usually strict) subset of semantic garbage,...

2000. ISBN 9780393322293. Davis, Martin (2004). The Undecidable : Basic papers on undecidable propositions, unsolvable problems and computable functions...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

answering that question. In modern terms, Hilbert's tenth problem is an undecidable problem. In a Diophantine equation, there are two kinds of variables:...

context-sensitive grammars (given a context-sensitive grammar G, is L(G)=∅ ?) is undecidable. Savitch has proven the following theoretical result, on which he bases...

difference is, that it becomes undecidable whether a specific function definition defines a μ-recursive function, as it is undecidable whether a computable (i...

Product Puzzle", which is not impossible -gry, a word puzzle List of undecidable problems, no algorithm can exist to answer a yes–no question about the...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

refers to three "aporias": "the epoche of the rule", "the ghost of the undecidable", and "the urgency that obstructs the horizon of knowledge". Aporia is...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

{\textsf {P}}\subsetneq {\textsf {P/poly}}} (for example, there are some undecidable problems that are in P/poly). P/poly has a number of properties that...

the halting problem is undecidable, the problem of deciding whether a Wang domino set can tile the plane is also undecidable. Truchet tiles are square...

generates a given string whether a W-grammar generates no strings at all are undecidable. Curtailed variants, known as affix grammars, were developed, and applied...

the halting problem for particular cases, since the general problem is undecidable. It provides a solution which is sound, meaning that when it states that...

from them—even though the abstraction may simply yield a result of undecidability. For instance, students in a class may be abstracted by their minimal...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Oha, Obododimma (2008-01-01), "Language, Exile and the Burden of Undecidable Citizenship: Tenzin Tsundue and the Tibetan Experience", Exile Cultures...

logician and philosopher Newton da Costa) is the proof that chaos theory is undecidable (published in 1991), and when properly axiomatized within classical set...

"in-between bits, the judders and rumbles and low howls drifting somewhere undecidable between composed music and sound design ... the un-music, the audiable...

be computable. Moreover, the equality of two computable numbers is an undecidable problem. Some constructivists accept the existence of only those reals...

non-commutative) local ring is free. Sometimes, whether a module is free or not is undecidable in the set-theoretic sense. A famous example is the Whitehead problem...

poetry can be read as queer even if the question of her lesbianism is undecidable. In antiquity, Sappho's poetry was highly admired, and several ancient...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

higher intersection types, typability becomes undecidable, in general. Complementarily, undecidability of the dual problem of type inhabitation in prominent...

non-classical logic. Amongst his most notable accomplishments is the proof of undecidability of the relevance logic R. He published numerous scientific papers in...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

addition and multiplication) is incompletable and hence a posteriori undecidable. Hao Wang praised Skolem's work as follows: Skolem tends to treat general...

(unstable, unbalanced, not measurable), and anepikrita (unjudged, unfixed, undecidable). Therefore, neither our sense-perceptions nor our doxai (views, theories...

which are sometimes called Culik–Yu classes; membership in these proved undecidable. Wolfram's class 2 can be partitioned into two subgroups of stable (fixed-point)...

about it. Known results include: The rank problem is algorithmically undecidable for the class of all finitely presented groups. Indeed, by a classical...

2008. and "Perl is Undecidable". The Perl Review. 5: 7–11. Fall 2008., available online at Kegler, Jeffrey. "Perl and Undecidability". Archived from the...

queries. Solving the boundedness problem on arbitrary Datalog programs is undecidable, but it can be made decidable by restricting to some fragments of Datalog...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

(unstable, unbalanced, not measurable), and anepikrita (unjudged, unfixed, undecidable). Therefore, neither our sense-perceptions nor our doxai (views, theories...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

elected in 2012 Chauvenet Prize: the 2011 winner, for his article "Undecidability in number theory" Miller Research Professorship – University of California...

proper (i.e. P ⊊ {\displaystyle \subsetneq } P/poly) because there are undecidable problems that are in P/poly. P/poly turns out to have a number of properties...

of Authority’”, Derrida emphasizes the relation between decision and undecidability, and the tension between normativity and singularity. This interpretation...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

is homeomorphic to another fixed simplicial complex. The problem is undecidable for complexes of dimension 5 or more. An abstract simplicial complex...

indiscernible, this generic point; and thus nominate, and give name to, the undecidable event. Badiou thereby marks out a philosophy by which to refute the apparent...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

attempt: "his authority as a story-teller to decide the historically undecidable mystery of Chatterton's death" Thus, "Chatterton is not a novel on the...

of proofs. According to the mode deriving from dispute, we find that undecidable dissension about the matter proposed has come about both in ordinary...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Emil Post later termed 'Thue Systems', and gave an early example of an undecidable problem. Post would later use this paper as the basis for a 1947 proof...

Old Series. 4 (3): 12. Padamalangula, Namphueng (2003). The play of undecidability: A deconstructive analysis of "Traiphum Phra Ruang"("Three Worlds According...

{\displaystyle {\mathsf {ZFC}}} remains unknown. List of statements undecidable in Z F C {\displaystyle {\mathsf {ZFC}}} Gelfand–Naimark theorem Akemann...

time itself may not be predictable by a halting program, due to the undecidability of the halting problem. He also explicitly discusses the more restricted...

Emperors (divus). The etymology of flamen remains obscure, and perhaps undecidable. The term is traditionally connected with the Proto-Germanic verb *blōtaną...

the mathematician Raphael Douady, he called the problem statistical undecidability (Douady and Taleb, 2010). Taleb has described his main challenge as...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

expression language from its grammar. Furthermore, it is algorithmically undecidable whether the language recognized by a parsing expression grammar is empty...

a free play but from the necessity of analysis. Derrida called these undecidables—that is, unities of simulacrum—"false" verbal properties (nominal or...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

structure of the network. Other topics in Moore's research include modeling undecidable problems by physical systems, phase transitions in random instances of...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

terms of computability. This means that quantum computers cannot solve undecidable problems like the halting problem, and the existence of quantum computers...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

are newcomers to the book. Some readers see the book as oscillating undecidably between these alternatives, like the Rubin vase (a drawing that may be...

number that encodes the solution of the halting problem (or any other undecidable problem) according to a chosen encoding scheme. Chaitin's constant, Ω...

arbitrary Turing machine, determining whether it is a decider is an undecidable problem. This is a variant of the halting problem, which asks for whether...

ISBN 0-7923-6151-2, pages 221–230. Martin Davis, 1965. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions...

the stranger as the person who is present yet unfamiliar, society's undecidable. In Modernity and Ambivalence Bauman attempted to give an account of...

Classical Quarterly, 52 (2002): 248–56. Svavarsson, Svavar Hrafn, "Pyrrho's undecidable nature", Oxford Studies in Ancient Philosophy, 27 (2004): 249–295. Library...

provided us with the right preconceptions. Weinberg believed that any undecidability in mathematics, such as the continuum hypothesis, could be potentially...

doi:10.1007/978-4-431-55639-8 Scholte, T. (2019). "Heuristics for the Undecidable." She Ji: The Journal of Design, Economics, and Innovation, 5(4), 379–382...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

the meaning of the pre-defined (RDF or OWL) vocabulary. OWL Full is undecidable, so no reasoning software is able to perform complete reasoning for it...

theoretical computer science, such as the proof that the halting problem is undecidable. Ken Thompson started development on Unix in 1968 by writing and compiling...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

only semi-effective for first-order logic, since first-order logic is undecidable, as showed by Church's theorem. This method is considered by many to...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

atom (fact) is entailed by a DatalogZ program is RE-complete (hence, undecidable), which can be shown by a reduction to diophantine equations. The syntax...

Sequence Charts (MSC), where it was shown that weak realizability is undecidable for bounded MSC-graphs and that safe-realizability is in EXPSPACE, along...

Determining whether a callable has a side effect is difficult – indeed, undecidable by virtue of Rice's theorem. So, while this optimization is safe in a...

rules. It shows that even though the question of safety is in general undecidable, for specific systems it is decidable in linear time. The model represents...

expressible in closed-form from elementary functions Richardson's theorem – Undecidability of equality of real numbers Stanley Burris, Simon Lee, Tarski's high...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

did research on the interface between algebra and logic, focusing on undecidability in group theory. At the time of her death, she was emeritus faculty...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

unwieldy characterisations of equality (which in most cases must also be undecidable, as a consequence of the halting problem). Bisimulations are a technical...

Halting problem Correctness Post correspondence problem Decidable language Undecidable language Word problem for groups Wang tile Penrose tiling Computable...

ISSN 0956-7968. since the halting problem for the latter class was proven to be undecidable "What to know before debating type systems | Ovid [blogs.perl.org]"....

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

exists a finitely presented group G such that the word problem for G is undecidable. A different proof was obtained by Boone in a paper published in 1958...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

the time hierarchy theorem. In computability theory, one of the basic undecidable problems is the halting problem: deciding whether a deterministic Turing...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

w_{m})\in R(S)} . Most problem related to perfect channel system are undecidable. This is due to the fact that such a machine may simulates the run of...

Company. ISBN 0-7167-2064-7. Davis, Martin (1965). The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions...

Turing machine running an algorithm that terminates on all inputs. An undecidable problem is a problem that is not decidable. As noted above, every context-sensitive...

modulus of convergence is undecidable. In recursion theory, the limit lemma proves that it is possible to encode undecidable problems using limits. There...

combined logic S4.1 (in fact, even K4.1) is canonical. In general, it is undecidable whether a given axiom is canonical. We know a nice sufficient condition:...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

decidable set of modal formulas with first-order correspondents. Since it is undecidable, by Chagrova's theorem, whether an arbitrary modal formula has a first-order...

Bałus, Wojciech (1994). "Dürer's 'Melencolia I': Melancholy and the Undecidable". Artibus et Historiae. 15 (30): 9–21. doi:10.2307/1483470. JSTOR 1483470...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

of paradoxes Self-reference Halting problem – the usual proof of its undecidability uses a similar contradiction Barile, Margherita. "Crocodile's Dilemma...

The decision problem of whether an arbitrary grammar is ambiguous is undecidable because it can be shown that it is equivalent to the Post correspondence...

Her dissertation showed that the theory of the rational numbers was an undecidable problem, by demonstrating that elementary number theory could be defined...

that this problem is undecidable; consequently, any word problem that has a reduction from this basic problem is likewise undecidable. Combinatorics on words...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

natural numbers form a set one may quantify over), then set-bounded but undecidable propositions can be expressed. In constructive type theory, or in Heyting...

the grammar. The latter problem is called the halting problem and is undecidable. Recursively enumerable languages are closed under Kleene star, concatenation...

ISBN 978-0-86171-396-7 Oha, Obododimma (2008), "Language, Exile, and the Burden of Undecidable Citizenship: Tenzin Tsundue and the Tibetan Experience", in Allatson...

some impractical problems, including some undecidable problems such as the unary version of any undecidable problem. In 1999, Jin-Yi Cai and D. Sivakumar...

inequalities is undecidable. Ray tracing in 3-D optical systems with a finite set of rectangular reflective or refractive objects is undecidable. Ray tracing...

is that which constitutes a text in a particular way. The text is an undecidable (there is an inexistence of an effective or "strict" method of writing...

(6)/\operatorname {SO} (5)=\operatorname {SU} (3)/\operatorname {SU} (2)} ⁠. It is undecidable whether a given ⁠ n {\displaystyle n} ⁠-dimensional manifold is homeomorphic...

nonuniversal Turing machines whose individual halting problems are nevertheless undecidable. A polynomial-time many-one reduction from a problem A to a problem B...

that Σ is not a computable function. Moreover, this implies that it is undecidable by a general algorithm whether an arbitrary Turing machine is a busy...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Order Logic, the more probable that it will allow expressions that are undecidable or require exponential processing power to complete. In the implementation...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

equal. Moreover, determining if ρ ≤ 1 {\displaystyle \rho \leq 1} is an undecidable problem. Nevertheless, in recent years much progress has been done on...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

concentration-based probability for which reaction will occur next) is undecidable. More specifically, a limited Turing machine can be simulated with arbitrarily...

might contain the solution to the halting problem or some other Turing-undecidable problem. Such an infinite tape of data is called a Turing oracle. Even...

Bounded Degree" 2021 Moritz Lichter and Jamie Tucker-Foltz 2022 Elena Di Lavore and Yoàv Montacute 2024 Søren Brinck Knudstorp "Relevant S is Undecidable"...

planning is strictly more expressive than STRIPS, to the point of being undecidable in the general case. However, many syntactic restrictions of HTN planning...

dependent types type checking remains decidable, but type inference becomes undecidable. Dependent ML has been superseded by ATS and is no longer under active...

227–244, doi:10.1215/00294527-2009-009, MR 2572972 Tarski, Alfred (1953), Undecidable theories, Studies in Logic and the Foundations of Mathematics, Amsterdam:...

is essentially undecidable because Q is, and every consistent theory whose theorems include the ST axioms is also essentially undecidable. This includes...

states that, for any nontrivial property P of partial functions, it is undecidable whether a given Turing machine computes a function with property P. The...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

fragment of first-order logic without function symbols, satisfiability is undecidable. The two-variable fragment of first-order logic with no function symbols...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

which suggested an argument that the continuum hypothesis is either undecidable or false in the sense of mathematical platonism. Woodin criticizes this...

is unreachable is at least as hard as the halting problem and hence undecidable Debray, Saumya K.; Evans, William; Muth, Robert; De Sutter, Bjorn (1...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

calculated. Specific instances cannot be given but this follows from the undecidability of the halting problem. For instance, if Goldbach's conjecture is true...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

2025-04-17. Froneman, Willemien (2010). "Composing According to Silence: Undecidability in Derrida and Cage's Roaratorio". IRASM. 41 (2): 293–317. Notes towards...

{\displaystyle A} is provable. If a theory with the disjunction property has undecidable propositions, the excluded middle disjunctions of some excluded middle...

automata with other non-block neighborhood structures, for which it is undecidable whether the automaton is reversible and for which the reverse dynamics...

of proofs. According to the mode deriving from dispute, we find that undecidable dissension about the matter proposed has come about both in ordinary...

in English as "On Intuitionistic Arithmetic and Number Theory" in The Undecidable, edited by M. Davis, pp. 75–81. Kolmogorov, Andrey Nikolaevich (1925)...

fragments, showing for instance that many expressive group STIT logics are undecidable or of high computational complexity. In the 2010s, STIT ideas were combined...

the word problem in group theory, which is known to be algorithmically undecidable. In fact, there is no algorithm for deciding whether a given manifold...

exists (i.e., whether the complete substitution set is nonempty) is undecidable. The set S is called minimal if none of its members subsumes another...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

However, if membership in a language is undecidable, then membership in its unary version is also undecidable. TALLY is contained in P/poly—the class...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

more generally, a set of EDs), and, if it terminates (which is a priori undecidable), output an instance that does satisfy the EGDs. An important subclass...

Media. ISBN 978-981-4021-07-4. Svozil, Karl (1993). Randomness and Undecidability in Physics. WORLD SCIENTIFIC. Bibcode:1993rup..book.....S. doi:10.1142/1524...

the discovery that optimal play in certain multiplayer games can be an undecidable problem. A third part of the book provides a compendium of known hardness...

false by using the axioms. However, note that in some cases it may be undecidable if a statement can be proven or not. A model for an axiomatic system...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

inference in the absence of any programmer supplied type annotation, is undecidable and functions defined over GADTs do not admit principal types in general...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

See temporal modal logic. Church's theorem A theorem establishing the undecidability of certain decision problems in logic, such as the Entscheidungsproblem...

minimization techniques, FSMs, Turing machines, Markov processes, and undecidability. Excellent treatment of Markov processes pp. 449ff. Discusses Z-transforms...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

concepts may be paradoxical or self-undermining, rendering their meaning undecidable. To extend this notion, deconstruction and the practice of sous rature...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

(Adleman's theorem). It also contains some undecidable problems, such as the unary version of every undecidable problem, including the halting problem. Because...

 29–122. Section 4.1: Decidable Languages, pp. 152–159. Section 5.1: Undecidable Problems from Language Theory, pp. 172–183. Elaine Rich (2008). Automata...

science makes him uncomfortable indeed with ambiguity, not to mention undecidability." Kahr called the book a "vicious piece of rhetoric" and argued that...

existential (i.e. Σ 1 1 {\displaystyle {\Sigma }_{1}^{1}} ) MSO theory is undecidable if we allow predicates on both vertices and edges. Thus, in a sense,...

the above is that it is undecidable whether a (positive) range concatenation language is nonempty, because it is undecidable whether the intersection...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

[UK]: Acumen. pp. 108–109. ISBN 978-1-84465-409-3. OCLC 715184861. Undecidability and the ten modes As part of his Pyrrhonian revival Aenesidemus assembled...

equivalent to the axiom of choice (that is, their truth values in ZF, while undecidable, are the same as that of AC). The most important among them are Zorn's...

equality, which requires proof. As a consequence type checking becomes undecidable in extensional type theory because programs in the theory might not terminate...

configuration? They showed that there is no such algorithm, thus the problem is undecidable in the general case. They also showed a limitation of the model to commands...

Springer. ISBN 978-3-319-75620-2. de Acosta, Alejandro (2009). "Two undecidable questions for thinking in which anything goes". In Randall Amster (ed...

problem will require, and explain why some problems are intractable or undecidable. Solvable computational problems belong to complexity classes that define...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

University Press: 596–616. Hirzel, Martin (trans.), 2000, "On formally undecidable propositions of Principia Mathematica and related systems I.". 1951,...

10, no. 4 (2004). Accessed 21 August 2023. See article On Formally Undecidable Propositions of Principia Mathematica and Related Systems and Gödel 1931...

Penguin Books. ISBN 0-14-01-4534-6. Gödel, Kurt (1992). On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Reprint ed...

Problems in Mathematics", in Davis, Martin (ed.), The undecidable. Basic papers on undecidable propositions, unsolvable problems and computable functions...

not decidable. This first such set, used by Berger in his proof of undecidability, required 20,426 Wang tiles. Berger later reduced his set to 104, and...

(complexity) NP-completeness NP-hardness EXPTIME PSPACE BPP (complexity) BQP Undecidable problem Halting problem Rice's theorem No free lunch theorem List of...

isomorphism in second homology is induced by some diffeomorphism. It is undecidable if a given 5-manifold is homeomorphic to S 5 {\displaystyle S^{5}} ,...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

of the principle was given by Stephen Wolfram in February 1985. In Undecidability and Intractability in Theoretical Physics , Wolfram wrote that "[U]niversal...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

equality of two functions is equivalent to the halting problem, and is undecidable, but equality of two functions in FP is just equality in the algebra...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

(1957, space science) Pyotr Novikov (1957, mathematics, for proving the undecidability of the word problem for groups) Sergei Prokofiev (1957, music, posthumously...

few, most notably Cantor's continuum hypothesis, have been shown to be undecidable on the basis of currently accepted principles. In 1931, Gödel's incompleteness...

foundations of mathematics. His work was largely on recursion theory and undecidability. From 1946 until his death in Vancouver, British Columbia, Canada, he...

earlier sections was decidable, adding the quantifiers makes the logic undecidable. So far, the quantified extensions are first-order: they distinguish...

unsolved problems List of lemmas List of theorems List of statements undecidable in ZFC Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Nei Y.; Castro, Paulo A. L. (2025). "Machines that halt resolve the undecidability of artificial intelligence alignment". Scientific Reports. 15 (1): 15591...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

LL(k) and LR(k) parsers, the problem of generating an LLR/LRR parser is undecidable unless one has constructed a regular partition upfront. But even the...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

what he called "P" (nowadays called Peano Arithmetic), "there exist undecidable sentences [propositions]". Because of this, "the consistency of P is...

ISBN 978-0-387-74640-1 Kurtz, Stuart A.; Simon, Janos (2007). "The Undecidability of the Generalized Collatz Problem". In Cai, Jin-Yi; Cooper, S. Barry;...

number theory. One stark difference is that Diophantine equations have an undecidable solubility problem, whereas the analogous problem for word equations...

dependencies that can be inclusion dependencies or functional dependencies is undecidable by reduction from the word problem for monoids. Declarative referential...

Decidability of first-order monadic predicate logic (Leopold Löwenheim 1915) Undecidability of first-order predicate logic (Church's theorem 1936) Other important...

interpreted predicate letters: both logics are sound, complete, and undecidable. Most work Quine published on logic and mathematics in the last 30 years...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

whose putative volume (rectangular, trapezoidal?) is ocularly quite undecidable. This great sheet of windows, with its gravity-defying two-dimensionality...

LL}}-({\mbox{RE}}\cup {\mbox{co-RE}})} . Not only are these problems undecidable, but neither they nor their complement are recursively enumerable. In...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

property of being well-typed is decidable. However, type inference is undecidable. A logic is represented in the LF logical framework by the judgements-as-types...

about the existence of a finitely presented group with algorithmically undecidable word problem also substantially use HNN-extensions. The idea of HNN extension...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

For instance, type inference for rank-3 and above system F remains undecidable (as detailed above), however, for intersection types, type inference...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

integration in terms of elementary functions Richardson's theorem – Undecidability of equality of real numbers Symbolic integration – Computation of an...

May 28 - Alan Turing submits "On Computable Numbers", proving the undecidability of the Halting problem and the decision problem for logic. Computer...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

techniques, finite-state machines, Turing machines, Markov processes, and undecidability. Booth studied at the University of Connecticut, where he received his...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

shown that the question of solvability of a Diophantine equation is undecidable even if the equation only has 9 natural number variables (Matiyasevich...

concepts may be paradoxical or self-undermining, rendering their meaning undecidable Jacques Derrida, Paul de Man, J. Hillis Miller, Philippe Lacoue-Labarthe...

possible that B is an undecidable problem for which no algorithm exists. M. Davis, ed., 1965. The Undecidable—Basic Papers on Undecidable Propositions, Unsolvable...

in contrast to DL's open world assumption. Also, F-logic is generally undecidable,[citation needed] whereas the SHOIN description logic that Web Ontology...

closure algebras undecidable. Naturman demonstrated that the theory is hereditarily undecidable (all its subtheories are undecidable) and demonstrated...

(locally symmetric spaces) Daniel Lacombe, Théorèmes de non-décidabilité (undecidability) Pierre Samuel, Travaux d'Igusa sur les formes modulaires de genre 2...

technical logic terms such as tiyuvta "conclusive refutation" and tiqu "undecidable moot point", which are still used in Jewish legal writings, including...

locations can also be shown to be PSPACE-complete, whereas the problem is undecidable with interpreted memory locations (e.g., integers) or further quantifier...

unrestricted recursion and are Turing complete, which makes the halting problem undecidable, can cause unsoundness of equational reasoning, and generally requires...

consistency. Verifying sequential consistency through model checking is undecidable in general, even for finite-state cache coherence protocols. Causal consistency...

the London Mathematical Society, Series 2, Volume 42 (1937), p.230–265. Reprinted in M. Davis (ed.), The Undecidable, Raven Press, Hewlett, NY, 1965....

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

supertypes in some contract. This definition of subtyping is generally undecidable, so it cannot be verified by a type checker. The subtyping of mutable...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

it is an undecidable problem to determine, given a finite presentation of a group, whether the group is Hopfian. Unlike the undecidability of many properties...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

automata it is not surprising that simple reachability questions are undecidable for general hybrid automata. In fact, a straightforward reduction from...

empties the place when the transition fires; this makes reachability undecidable, while some other properties, such as termination, remain decidable;...

quantum box can have a perfect score at a non-local game is known to be undecidable. Moreover, the problem of deciding whether P ( a , b | x , y ) {\displaystyle...

Edwards left Apple in April 2014 and founded a new stealth startup Undecidable Labs in 2015 with some ex-Chomp colleagues which was acquired by Google...

set-up can be used to decide the halting problem, which is known to be undecidable by an ordinary Turing machine. All the observer needs to do is to prime...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

considered a practical class for computing. Indeed, it contains every undecidable unary language, none of which can be solved in general by real computers...

mathematics (e.g. Peano Arithmetic), there are statements which are undecidable. In that context, it is difficult to state that "all truths are knowable"...

equivalent to a language with a different grammar. The following problems are undecidable for arbitrarily given context-free grammars A and B: Equivalence: is...

problem for programs of length up to n. Since the halting problem is undecidable, Ω cannot be computed. The algorithm proceeds as follows. Given the first...

He used it to confirm Gödel by proving that the halting problem is undecidable. 1940 Edward Condon displayed Nimatron, a digital machine that played...

Truth, would be a falsity, an insanity.) Proposition VI, On Formally Undecidable Propositions in Principia Mathematica and Related Systems I (1931) Casti...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

answer to the program. If arbitrary propagation is allowed, reasoning is undecidable and the program will be infinite. Warded Datalog± overcomes this issue...

the equality of two real numbers given by an expression is known to be undecidable (specifically, real numbers defined by expressions involving the integers...

studies Scientific method The Analyst Euclid's Elements "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" "On Computable...

constrained Horn clauses with constraints from linear integer arithmetic is undecidable. There are several automated solvers for CHCs, including the SPACER engine...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

disproof of Goldbach's conjecture must exist (the conjecture may be undecidable in traditional ZF set theory). Thus to Brouwer, we are not justified...

structures than graphs is chosen). Termination for DPO graph rewriting is undecidable because the Post correspondence problem can be reduced to it. DPO graph...

121–123. doi:10.1093/analys/23.6.121. Gödel, Kurt (1931). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Basic Books...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

This defines a metalanguage stack of increasing capability to resolve undecidability in the autonomous lower levels. If someone near process level needs...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

theory. Furthermore, under Field's nominalization, statements that are undecidable in standard set theory like the continuum hypothesis become statable...

ISBN 978-0-262-02649-9. LCCN 2007037603. Jančar, Petr; Srba, Jiří (2008). "Undecidability of Bisimilarity by Defender's Forcing". J. ACM. 55 (1). New York, NY...

{N} } ,+)) can interpret the true second-order arithmetic and is thus undecidable. Just as in first-order logic, second-order logic may include non-logical...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

{\displaystyle L\in \mathbb {C} } has a characteristic sample. If equivalence is undecidable for a class C {\textstyle \mathbb {C} } over Σ {\textstyle \Sigma } of...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

determine if the predicate is a contradiction or not. Since this problem is undecidable, the tool implements a best-effort algorithm that can be improved by...

proved that the classical halting problem for Turing machines, although undecidable, is nevertheless decidable on a set of asymptotic probability one, one...

that a given expression is non-zero, or of showing that the problem is undecidable. For example, if x1, ..., xn are real numbers, then there is an algorithm...

Springer-Verlag, ISBN 978-0-387-90170-1 Smullyan, Raymond M. (1958), "Undecidability and recursive inseparability", Zeitschrift für Mathematische Logik und...

Whitehead, Principia Mathematica, 1910–13/1925–27 Kurt Gödel, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems", 1931 Alfred...

sort, would be considered equal. Deciding on extensional equality is undecidable in general and even for functions with finite domains often intractable...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Entscheidungsproblem by first showing that the halting problem for Turing machines is undecidable: in general, it is not possible to decide algorithmically whether a given...

was eventually stymied by the phenomenon that many basic problems are undecidable. Despite tracing the origins of automatic groups to early 20th-century...

known as the Church-Turing Thesis and proved that first-order logic is undecidable. 1962 Clark, Wesley A. Designed LINC, the first functional computer scaled...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

string y such that x[T]y for a given string x.[citation needed] It is undecidable whether two transducers are equivalent. Equivalence is however decidable...

{\displaystyle \beth _{\alpha }} can exist. (In that case, the existence is undecidable in ZFC and controlled by the Generalized Continuum Hypothesis.) Even...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

PSPACE-complete. For other calculi, like System F, the problem is even undecidable. Curry–Howard isomorphism Pawel Urzyczyn (1997). "Inhabitation in typed...

properties of those systems are undecidable and Gödel-incomplete, that is, a sentence like X is chaotic is undecidable within that axiomatics. They later...

propositions of number theory, such as Goldbach's conjecture, or even undecidable propositions could be determined in a finite amount of time by a brute-force...

termination, type argument inference, and ambiguous programs. In general it is undecidable whether a Java program using generics is well-typed or not, so any type...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

denotes unconsumable resources. The entailment relation in full CLL is undecidable. When considering fragments of CLL, the decision problem has varying...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

cellular automata and for one-dimensional cellular automata, but is undecidable for other types of cellular automata. Reversible cellular automata form...

Press, ISBN 0-19-853189-3. Martin Davis, ed. (1965). The Undecidable – Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions...

to applications of double-negation elimination. In particular, with undecidable atomic propositions being absent, for any proposition ψ {\displaystyle...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

cannot be derived from this case (since it involves deciding potentially undecidable problems), but the proof of Adleman's theorem can be easily adapted to...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

with arbitrary demands is a hard problem, which can be NP-hard and even undecidable. In a linear network coding problem, a group of nodes P {\displaystyle...

between the human and the technical, the "who" and the "what" are in an undecidable relation. Part II is largely a reading of the work of Martin Heidegger...

provable formulas . . . ." (p. 72 in Martin Davis ed. The Undecidable: "Postscriptum" to "On Undecidable Propositions of Formal Mathematical Systems" appearing...

automata. The asymptotic behavior of these PDEs is therefore logically undecidable. With John David Crawford he showed that the orbits of three-dimensional...

Church proved additional undecidability results, showing that both Peano arithmetic and first-order logic are undecidable. Later work by Emil Post and...

vectors can have positive as well as negative coefficients, it is an undecidable problem to determine whether two such games have the same P-positions...

403 pages 175–179, 2000. O. Madani, A. Condon, and S. Hanks, "On the Undecidability of Probabilistic Planning and Infinite-Horizon Partially Observable...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

whether a program will halt on a particular input, or on all inputs, is undecidable. Therefore, a general algorithm for proving any program to halt does...

is justified if one is presented with a question which is rationally undecidable and if one is presented with genuine and live options which are relevant...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Daniel Peralta-Salas and collaborators, she showed the existence of undecidable fluid paths, linking computer science, differential geometry, and fluid...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

enumerable Computable function Computable set Decision problem decidable undecidable P NP P versus NP problem Kolmogorov complexity Lambda calculus Primitive...

Geoffrey K. (2000) "Scooping the loop snooper: An elementary proof of the undecidability of the halting problem". Mathematics Magazine 73.4 (October 2000), 319–320...

given a description of a polynomial-time probabilistic machine, it is undecidable in general to determine if it recognizes a language in BPP. PP has natural...