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 Deterministic Algorithm for SAT
Proceedings of the 12th International Workshop on Computer Science Logic
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
A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms
IEEE Annals of the History of Computing
On an optimal propositional proof system and the structure of easy subsets of TAUT
Theoretical Computer Science - Complexity and logic
On the Structure of the Simulation Order of Proof Systems
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Is the Standard Proof System for SAT P-Optimal?
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
On a P-optimal Proof System for the Set of All Satisfiable Boolean Formulas (SAT)
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
Nondeterministic functions and the existence of optimal proof systems
Theoretical Computer Science
On slicewise monotone parameterized problems and optimal proof systems for TAUT
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
On an optimal randomized acceptor for graph nonisomorphism
Information Processing Letters
Optimal acceptors and optimal proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
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A deterministic algorithm O accepting a language L is called (polynomially) optimal if for any algorithm A accepting L there is a polynomial p such that timeO(x) ≤ p(|x|+ timeA(x)) for every x ∈ L. It is shown that an optimal acceptor for a language L exists if there is a p-optimal proof system for L. If L is a p-cylinder also the inverse implication holds. This result widely generalizes work from Krajíček and Pudlák who showed the result for L = TAUT. It is further shown how to construct an optimal acceptor for a p-cylinder L, given an acceptor for L which runs fast on every easy subset of L. Then we investigate the relationship of this notion of an 'optimal acceptor' to a more general notion of optimality. Here, instead of considering time-complexity on each individual string x, worst-case time-bounds are considered. It is observed that every set complete for exponential time under linearly length-bounded polynomial-time many-one reducibility has an acceptor with an optimal time-bound whereas on the other hand no set hard for exponential time under polynomial-time many-one reducibility has a p-optimal proof system. Finally we show how these results can be translated to nondeterministic algorithms and optimal proof systems.