Post correspondence problem
E679187
computability theory problem
decision problem
problem in theoretical computer science
undecidable problem
The Post correspondence problem is a classic undecidable decision problem in theoretical computer science and mathematical logic that plays a central role in demonstrating the limits of algorithmic computability.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
computability theory problem
ⓘ
decision problem ⓘ problem in theoretical computer science ⓘ undecidable problem ⓘ |
| alphabetSizeCondition | undecidable for alphabet of size at least 2 ⓘ |
| appearsIn |
formal languages and automata theory courses
ⓘ
introductory computability theory textbooks ⓘ |
| boundedVariant | NP-complete ⓘ |
| centralConcept |
Turing computability
ⓘ
algorithmic unsolvability ⓘ reduction ⓘ undecidability ⓘ |
| completeFor | recursively enumerable sets under many-one reductions ⓘ |
| complexityClass | RE-complete ⓘ |
| decisionQuestion | existence of a matching sequence of indices ⓘ |
| definedOver | finite alphabet ⓘ |
| dominoCountCondition | undecidable for sufficiently many dominoes ⓘ |
| field |
computability theory
ⓘ
mathematical logic ⓘ theoretical computer science ⓘ |
| hasInput |
finite list of pairs of strings
ⓘ
finite set of dominoes ⓘ |
| hasVariant |
bounded Post correspondence problem
ⓘ
modified Post correspondence problem NERFINISHED ⓘ |
| introducedBy | Emil Post NERFINISHED ⓘ |
| language | formal language theory ⓘ |
| namedAfter | Emil Post NERFINISHED ⓘ |
| output | yes or no ⓘ |
| property |
not decidable
ⓘ
recursively enumerable ⓘ semi-decidable ⓘ |
| publication | A variant of a recursively unsolvable problem ⓘ |
| question | whether there exists a sequence of dominoes forming equal top and bottom strings ⓘ |
| relatedTo |
Post normal systems
NERFINISHED
ⓘ
Turing machines NERFINISHED ⓘ context-free grammars ⓘ halting problem NERFINISHED ⓘ tiling problem ⓘ word problem for semi-Thue systems ⓘ |
| role |
canonical example of an undecidable problem
ⓘ
tool for proving undecidability of other problems ⓘ |
| typicalReductionFrom |
halting problem
ⓘ
word problem for Post normal systems ⓘ |
| usedToProve |
undecidability of Post normal system properties
ⓘ
undecidability of context-free grammar equivalence ⓘ undecidability of problems in formal language theory ⓘ undecidability of the halting problem variants ⓘ |
| yearIntroduced | 1946 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.