TY - GEN

T1 - Optimal acceptors and optimal proof systems

AU - Hirsch, Edward A.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77954436597&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-13562-0_4

DO - 10.1007/978-3-642-13562-0_4

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:77954436597

SN - 3642135617

SN - 9783642135613

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 28

EP - 39

BT - Theory and Applications of Models of Computation - 7th Annual Conference, TAMC 2010, Proceedings

T2 - 7th Annual Conference on Theory and Applications of Models of Computation, TAMC 2010

Y2 - 7 June 2010 through 11 June 2010

ER -