Proving SAT does not have Small Circuits with an Application to the Two
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چکیده
We show that if SAT does not have small circuits, then there must exist a small number of satisfiable formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that if PNP[1] = PNP[2], then the polynomial-time hierarchy collapses to Sp2 ⊆ Σp2∩Πp2. Even showing that the hierarchy collapsed to Σp2 remained open prior to this paper.
منابع مشابه
Proving SAT does not have Small Circuits with an Application to the Two Queries Problem
We show that if SAT does not have small circuits, then there must exist a small number of formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that ifPNP[1℄ = PNP[2℄, then the polynomial-time hierarchy collapses to Sp2 p2 \ p2. Even showing that the hierarchy collapsed to p2 remained open prior to this paper.
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