Abstract not found

This is a survey of work on proof complexity and proof search, as motivated by the P versus NP problem. We discuss propositional proof complexity, Cook’s program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP.

Abstract. 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. 1 Introduction and basic definitions