On a P-optimal Proof System for the Set of All Satisfiable Boolean Formulas (SAT)
نویسنده
چکیده
In this paper we show that the problem of the existence of a p-optimal proof system for SAT can be characterized in a similar manner as J. Hartmanis and L. Hemachandra characterized the problem of the existence of complete languages for UP. Namely, there exists a p-optimal proof system for SAT if and only 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.
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