Structural complexity 1
Complexity classes without machines: on complete languages for UP
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
Structural complexity 2
A uniform approach to define complexity classes
Theoretical Computer Science
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Proceedings of the Mathematical Foundations of Computer Science 1984
Optimal Proof Systems for Propositional Logic and Complete Sets
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
On an Optimal Quantified Propositional Proof System and a Complete Language for NP cap co-NP
FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
Complete Problems for Promise Classes by Optimal Proof Systems for Test Sets
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
On the lengths of proofs in the propositional calculus (Preliminary Version)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Reductions between disjoint NP-pairs
Information and Computation
Classes of representable disjoint NP-pairs
Theoretical Computer Science
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
The Shrinking Property for NP and coNP
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Does Advice Help to Prove Propositional Tautologies?
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Nondeterministic functions and the existence of optimal proof systems
Theoretical Computer Science
Characterizing the Existence of Optimal Proof Systems and Complete Sets for Promise Classes
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Reductions between disjoint NP-Pairs
Information and Computation
The deduction theorem for strong propositional proof systems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Logical closure properties of propositional proof systems
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
On p-optimal proof systems and logics for PTIME
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
The shrinking property for NP and coNP
Theoretical Computer Science
Proof systems that take advice
Information and Computation
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Disjoint NP-pairs from propositional proof systems
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Optimal acceptors and optimal proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Different approaches to proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Representable disjoint NP-Pairs
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Survey of disjoint NP-pairs and relations to propositional proof systems
Theoretical Computer Science
From Almost Optimal Algorithms to Logics for Complexity Classes via Listings and a Halting Problem
Journal of the ACM (JACM)
A parameterized halting problem
The Multivariate Algorithmic Revolution and Beyond
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
the informational content of canonical disjoint NP-pairs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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A polynomial time computable function h : Σ* → Σ* whose range is a set L is called a proof system for L. In this setting, an h-proof for x ∈ L is just a string w with h(w) = x. Cook and Reckhow defined this concept in [13], and in order to compare the relative strength of different proof systems for the set TAUT of tautologies in propositional logic, they considered the notion of p-simulation. Intuitively, a proof system h' p-simulates h if any h-proof w can be translated in polynomial time into an h'-proof w' for h(w). We also consider the related notion of simulation between proof systems where it is only required that for any h-proof w there exists an h'-proof w' whose size is polynomially bounded in the size of w. A proof system is called (p-)optimal for a set L if it (p-)simulates every other proof system for L. The question whether p-optimal or optimal proof systems for TAUT exist is an important one in the field. In this paper we show a close connection between the existence of (p-)optimal proof systems and the existence of complete problems for certain promise complexity classes like UP, NP ∩ Sparse, RP or BPP. For this we introduce the notion of a test set for a promise class C and prove that C has a many-one complete set if and only if C has a test set T with a p-optimal proof system. If in addition the machines defining a promise class have a certain ability to guess proofs, then the existence of a p-optimal proof system for T can be replaced by the presumably weaker assumption that T has an optimal proof system. Strengthening a result from Krajícek and Pudlák [20], we also give sufficient conditions for the existence of optimal and p-optimal proof systems.