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
On reducibility and symmetry of disjoint NP pairs
Theoretical Computer Science - Mathematical foundations of computer science
Optimal proof systems imply complete sets for promise classes
Information and Computation
Hierarchy Theorems for Probabilistic Polynomial Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Foundations and Trends® in Theoretical Computer Science
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms
IEEE Annals of the History of Computing
Nondeterministic Instance Complexity and Proof Systems with Advice
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
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
Structural Complexity of AvgBPP
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
On optimal algorithms and optimal proof systems
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Verifying proofs in constant depth
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
On an optimal randomized acceptor for graph nonisomorphism
Information Processing Letters
Different approaches to proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Verifying proofs in constant depth
ACM Transactions on Computation Theory (TOCT)
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Unless we resolve the P vs NP question, we are unable to say whether there is an algorithm (acceptor) that accepts Boolean tautologies in polynomial time and does not accept non-tautologies (with no time restriction) Unless we resolve the co-NP vs NP question, we are unable to say whether there is a proof system that has a polynomial-size proof for every tautology. In such a situation, it is typical for complexity theorists to search for “universal” objects; here, it could be the “fastest” acceptor (called optimal acceptor) and a proof system that has the “shortest” proof (called optimal proof system) for every tautology Neither of these objects is known to the date. In this survey we review the connections between these questions and generalizations of acceptors and proof systems that lead or may lead to universal objects.