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- {{Short description|Computational problems no algorithm can solve}} ...e [[subset]]s of [[Alan Turing|Turing]] recognizable languages: i.e., such undecidable languages may be recursively enumerable. ...16 KB (2,113 words) - 17:14, 23 June 2025
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- #REDIRECT [[List of undecidable problems]] ...42 bytes (5 words) - 12:28, 19 December 2012
- *[[Decidable problem]] and [[Undecidable problem]] * [[List of undecidable problems]] ...552 bytes (61 words) - 15:04, 6 November 2022
- {{about|decision problems in complexity theory|the decision problem in formal logic|Entscheidungsprob ...of the most important problems in mathematics are '''[[undecidable problem|undecidable]]''', e.g. the [[halting problem]]. ...10 KB (1,508 words) - 09:36, 19 May 2025
- *[[List of statements undecidable in ZFC|List of statements undecidable in <math> \mathsf{ZFC} </math>]] [[Category:Unsolved problems in mathematics]] ...2 KB (287 words) - 06:41, 25 January 2024
- ...(complexity)|P]], [[NP (complexity)|NP]], NP-complete, and NP-hard set of problems. The left side is valid under the assumption that [[P versus NP problem|P≠N ...NP|P≠NP]], it is unlikely that any polynomial-time algorithms for NP-hard problems exist.<ref>{{cite book |author1=Daniel Pierre Bovet |title=Introduction to ...9 KB (1,304 words) - 00:05, 12 October 2025
- ...be any polynomial in ''n''. '''P/poly''' is equal to the class of decision problems such that, for every ''n'', there exists a polynomial size [[Boolean circui ...is equivalence, '''P/poly''' is sometimes defined as the class of decision problems solvable by polynomial size Boolean circuits, or by [[Circuit complexity#Un ...5 KB (683 words) - 05:39, 4 August 2023
- ...The Whitehead problem was the first purely algebraic problem to be proved undecidable. ...s the continuum hypothesis.{{r|Shelah1977|Shelah1980}} In fact, it remains undecidable even under the [[generalised continuum hypothesis]].<ref>{{cite web |url=ht ...6 KB (791 words) - 10:09, 14 June 2025
- ...ery natural number in a finite number of steps. A set is noncomputable (or undecidable) if it is not computable. {{Main|List of undecidable problems}} ...4 KB (580 words) - 23:17, 22 May 2025
- ...was identified by [[Max Dehn]] in 1911 as one of the fundamental decision problems in group theory; the other two being the [[Word problem for groups|word pro It is known that the conjugacy problem is [[undecidable problem|undecidable]] for many classes of groups. ...4 KB (536 words) - 01:02, 31 October 2024
- ...er a set of Wang tiles forms a valid tessellation is [[undecidable problem|undecidable]], and its undecidability rests on finding sets of Wang tiles that can only }}.</ref> Kari has also shown that the Wang tiling problem remains undecidable in the [[hyperbolic geometry#Models of the hyperbolic plane|hyperbolic plan ...6 KB (747 words) - 09:13, 24 April 2025
- The mathematical structure generated on a set of problems by the reductions of a particular type generally forms a [[preorder]], whos ...ly two numbers, we can square a number. This seems to imply that these two problems are equally hard. This kind of reduction corresponds to [[Turing reduction] ...11 KB (1,739 words) - 21:46, 20 April 2025
- Equivalently, '''RE''' is the class of decision problems for which a Turing machine can list all the 'yes' instances, one by one (th Not only are these problems undecidable, but neither they nor their complement are recursively enumerable. ...7 KB (1,039 words) - 14:58, 13 May 2025
- ...included in the theory. Many important problems are [[undecidable problem|undecidable]], that is, it has been proven that no effective method for determining mem ...-order logic, such as [[second-order logic]] and [[type theory]], are also undecidable. ...16 KB (2,160 words) - 21:01, 15 May 2025
- {{Short description|Computational problems no algorithm can solve}} ...e [[subset]]s of [[Alan Turing|Turing]] recognizable languages: i.e., such undecidable languages may be recursively enumerable. ...16 KB (2,113 words) - 17:14, 23 June 2025
- ...le=Unresolved systems of language equations: Expressive power and decision problems|journal=Theoretical Computer Science|volume=349|issue=3|pages=283–308|doi=1 ...ngs is hard, while doing the same for arbitrary context-free grammars is [[undecidable problem|completely impossible]]. However, it can still be efficiently deci ...8 KB (1,144 words) - 19:51, 26 August 2023
- ...ional problem without a solution is the [[Halting problem]]. Computational problems are one of the main objects of study in theoretical computer science. ...tractable]] or [[Undecidable problem|undecidable]]. Solvable computational problems belong to [[Complexity class|complexity classes]] that define broadly the r ...8 KB (1,121 words) - 22:51, 16 September 2024
- ...ze der Principia Mathematica und verwandter Systeme I'''" ("'''On Formally Undecidable Propositions of Principia Mathematica and Related Systems I'''") is a paper ...delson for [[Martin Davis (mathematician)|Martin Davis]]'s anthology ''The Undecidable''; but it too was not brought to Gödel's attention until almost the last mi ...11 KB (1,697 words) - 17:17, 16 October 2023
- ...all non-trivial semantic properties of programs are [[undecidable problem|undecidable]]. A ''semantic'' property is one about the program's behavior (for instanc Then <math>P</math> is [[undecidable problem|undecidable]]. ...12 KB (1,878 words) - 13:47, 14 November 2025
- ...[first-order logic]] on the class of all finite models is [[Recursive set|undecidable]]. In fact, the class of valid [[Sentence (mathematical logic)|sentences]] ...ntence of first-order logic that is satisfied in some finite structure} is undecidable. (p. 127, Th. 7.2.1 in <ref name=":0" />) ...11 KB (1,935 words) - 23:31, 14 April 2025
- **[[Undecidable language]] ==Named problems== ...5 KB (517 words) - 16:43, 14 March 2025