MIP equals NEXP
E364352
MIP equals NEXP is a landmark complexity-theoretic result showing that problems solvable by multi-prover interactive proofs exactly match those solvable in nondeterministic exponential time.
All labels observed (1)
| Label | Occurrences |
|---|---|
| MIP equals NEXP canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3522558 — 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: MIP equals NEXP Context triple: [PCP theorem, relatedTheorem, MIP equals NEXP]
-
A.
Interactive Proofs and the Hardness of Approximating Cliques
"Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
-
B.
Håstad’s switching lemma
Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
-
C.
The Knowledge Complexity of Interactive Proof Systems
"The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
-
D.
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.
-
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: MIP equals NEXP Target entity description: MIP equals NEXP is a landmark complexity-theoretic result showing that problems solvable by multi-prover interactive proofs exactly match those solvable in nondeterministic exponential time.
-
A.
Interactive Proofs and the Hardness of Approximating Cliques
"Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
-
B.
Håstad’s switching lemma
Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
-
C.
The Knowledge Complexity of Interactive Proof Systems
"The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
-
D.
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.
-
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 |
complexity-theoretic result
ⓘ
theorem in computational complexity theory ⓘ |
| assertsThat | MIP equals NEXP ⓘ |
| assumesComplexityMeasure | time complexity ⓘ |
| assumesModelOfComputation | Turing machine ⓘ |
| assumesProversAre | computationally unbounded ⓘ |
| assumesVerifierIs | probabilistic polynomial-time machine ⓘ |
| characterizes | power of multiple non-communicating provers ⓘ |
| comparesTo | IP = PSPACE ⓘ |
| describesClass |
languages decidable by multi-prover interactive proofs
ⓘ
languages decidable in nondeterministic exponential time ⓘ |
| equatesComplexityClass |
class of problems solvable by multi-prover interactive proofs
ⓘ
class of problems solvable in nondeterministic exponential time ⓘ |
| formalStatement | MIP = NEXP ⓘ |
| hasAbbreviation | MIP=NEXP ⓘ |
| hasAuthor |
Carsten Lund
ⓘ
Lance Fortnow ⓘ László Babai ⓘ Mario Szegedy ⓘ Shmuel Safra ⓘ |
| hasConsequence |
multi-prover interactive proofs are strictly more powerful than single-prover interactive proofs unless PSPACE = NEXP
ⓘ
nondeterministic exponential time problems admit multi-prover interactive proof systems ⓘ provides basis for later PCP theorem developments ⓘ |
| hasField |
computational complexity theory
ⓘ
theory of interactive proofs ⓘ |
| hasImpactOn |
design of probabilistically checkable proofs
ⓘ
understanding of interactive proof hierarchies ⓘ |
| hasYearOfPublication | 1991 ⓘ |
| impliesContainment |
MIP ⊆ NEXP
ⓘ
NEXP ⊆ MIP ⓘ |
| influences | subsequent work on multi-prover interactive proofs with entangled provers ⓘ |
| isCitedAs | Babai–Fortnow–Lund–Safra–Szegedy theorem ⓘ |
| isContrastedWith | MIP* = RE ⓘ |
| isLandmarkFor |
interactive proof systems
ⓘ
multi-prover interactive proofs ⓘ nondeterministic exponential time ⓘ |
| isProvedUsing |
algebraic encoding of computations
ⓘ
oracularization techniques ⓘ parallel repetition ideas ⓘ |
| isRelatedTo |
PCP theorem
ⓘ
hardness of approximation ⓘ |
| isTaughtIn | graduate complexity theory courses ⓘ |
| originallyAnnouncedIn | late 1980s ⓘ |
| publishedIn | Journal of the ACM ⓘ |
| relatesConcept |
MIP
ⓘ
NEXP ⓘ |
| statesEqualityBetween |
MIP
ⓘ
NEXP ⓘ |
| usesModel | multi-prover interactive proof system ⓘ |
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: MIP equals NEXP Description of subject: MIP equals NEXP is a landmark complexity-theoretic result showing that problems solvable by multi-prover interactive proofs exactly match those solvable in nondeterministic exponential time.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.