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Proof complexity

In logic and theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources that are required to prove or refute statements. Research in proof complexity is predominantly concerned with proving proof-length lower and upper bounds…

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Overview

Main concepts

Proof size complexity

Proof system strength

Results

Bounded arithmetic

SAT solvers

Lower bounds

Non-classical logics

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Proof complexity

Nodes80
Edges79
Triples62
Avg. degree1.98
Density0.025
Components1

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Proof complexity

Top relations

related to Further reading · 48
Proof complexity → Amsterdam, Applications, Beame, Bounded, Bulletin, Buss, Cambridge, Cambridge University Press, CBO9780511676277, ECCC TR98-067Cook, Encyclopedia, England, European Association, European Congress, European Mathematical Society, Foundations, Handbook, ISBN, Jan, Krajíček
related to Complexity · 4
Proof complexity → Boolean, In, Ordinary, Proof
related to Proof system strength · 2
Proof complexity → Efficiency, Proof
is a · 1
Proof complexity → field aiming to understand and analyse the computational resources that are required to prove or refute statements
related to External links · 1
Proof complexity → Proof ComplexityProof

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Important terminology

proof system displaystyle complexity systems propositional lower tautology resolution bounds size frege feasible interpolation phi proofs theory prove many automatable

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Proof complexityis afield aiming to understand and analyse the computational resources that are required to prove or refute statements0.90text
SAT solving.Mathematical logic can also serve as a framework to study propositional proof sizesinstance ofThis connects proof complexity to more applied areas0.80text
ZFC induce propositional proof systems as wellinstance ofStrong mathematical theories0.80text
Frege or constant-depth Frege.While the above-mentioned correspondence says that proofs in a theory translate to sequences of short proofs in the corresponding proof systeminstance ofhas been more practical for capturing subsystems of Extended Frege0.80text
a form of the opposite implication holds as wellinstance ofhas been more practical for capturing subsystems of Extended Frege0.80text
Resolutioninstance ofand dually to turn efficient interpolation algorithms into lower bounds on proof length.Some proof systems0.80text
Cutting Planes admit feasible interpolation or its variants.Feasible interpolation can be seen as a weak form of automatabilityinstance ofand dually to turn efficient interpolation algorithms into lower bounds on proof length.Some proof systems0.80text
Proof complexityrelated to ComplexityOrdinary0.60section
Proof complexityrelated to ComplexityProof0.60section
Proof complexityrelated to ComplexityIn0.60section
Proof complexityrelated to ComplexityBoolean0.60section
Proof complexityrelated to External linksProof ComplexityProof0.60section

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