P versus NP problem
E131016
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
All labels observed (1)
| Label | Occurrences |
|---|---|
| P versus NP problem canonical | 9 |
How this entity was disambiguated
This entity first appeared as the object of triple T1134458 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: P versus NP problem Context triple: [Avi Wigderson, hasResearchInterest, P versus NP problem]
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A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
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B.
P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
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C.
Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
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D.
PCP theorem
The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
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E.
“Inapproximability results for SAT and other problems”
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: P versus NP problem Target entity description: The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
-
A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
-
B.
P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
-
C.
Entscheidungsproblem
The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
-
D.
PCP theorem
The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
-
E.
“Inapproximability results for SAT and other problems”
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
computational complexity theory problem
ⓘ
open mathematical problem ⓘ |
| asksWhether | P equals NP ⓘ |
| concerns |
efficient solvability of decision problems
ⓘ
efficient verifiability of solutions ⓘ |
| difficultyBelief | Most experts believe P ≠ NP ⓘ |
| equivalentTo | asking whether NP-complete problems have polynomial-time algorithms ⓘ |
| field |
computational complexity theory
ⓘ
theoretical computer science ⓘ |
| formalizedIn |
Cook–Levin theorem
ⓘ
surface form:
Cook’s theorem
|
| formalStatement | Does P = NP? ⓘ |
| hasConsequence |
would affect feasibility of many optimization problems
ⓘ
would impact cryptography if P = NP ⓘ would revolutionize algorithms if P = NP ⓘ |
| hasPrize | 1 million US dollars ⓘ |
| importance |
central question in theoretical computer science
ⓘ
one of the most famous open problems in mathematics ⓘ |
| introducedBy |
Leonid Levin
ⓘ
Stephen Cook ⓘ |
| introductionYear | 1971 ⓘ |
| involvesComplexityClass |
NP
ⓘ
P ⓘ |
| knownImplication |
If P = NP then NP-complete problems are solvable in polynomial time
ⓘ
If P = NP then every problem in NP can be solved in polynomial time ⓘ If P ≠ NP then there exist problems in NP that cannot be solved in polynomial time ⓘ If any NP-complete problem is in P then P = NP ⓘ |
| openAsOf | 2024 ⓘ |
| partOf |
Millennium Prize Problem
ⓘ
surface form:
Millennium Prize Problems
|
| recognizedBy | Clay Mathematics Institute ⓘ |
| relatedConcept |
Cook–Levin theorem
ⓘ
NP-completeness ⓘ SAT problem ⓘ certificate of solution ⓘ decision problem ⓘ deterministic Turing machine ⓘ nondeterministic Turing machine ⓘ nondeterministic polynomial time ⓘ optimization problem ⓘ polynomial time ⓘ polynomial-time verifier ⓘ reduction between problems ⓘ search problem ⓘ verification algorithm ⓘ |
| relatedField |
algorithm design
ⓘ
cryptography ⓘ logic in computer science ⓘ proof complexity ⓘ |
| status |
major open problem
ⓘ
unsolved ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: P versus NP problem Description of subject: The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Introduction to Automata Theory, Languages, and Computation
subject surface form:
The Complexity of Theorem-Proving Procedures