On a P-optimal Proof System for the Set of All Satisfiable Boolean Formulas (SAT)

Authors:
Zenon Sadowski
Affiliations:
-
Venue:
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
Year:
2001

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Abstract

In this paper we show that the problem of the existence of a p-optimal proof system for SAT can be characterizedin a similar manner as J. Hartmanis andL. Hemachandra characterizedthe problem of the existence of complete languages for UP. Namely, there exists a p-optimal proof system for SAT if andonly if there is a suitable recursive presentation of the class of all easy (polynomial time recognizable) subsets of SAT. Using this characterization we prove that if there does not exist a p-optimal proof system for SAT, then for every theory T there exists an easy subset of SAT which is not T-provably easy.