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December 2007 Consequences of the provability of NPP/poly
Stephen Cook, Jan Krajíček
J. Symbolic Logic 72(4): 1353-1371 (December 2007). DOI: 10.2178/jsl/1203350791

Abstract

We prove the following results: (i) PV proves NPP/poly iff PV proves coNPNP/O(1). (ii) If PV proves NPP/poly then PV proves that the Polynomial Hierarchy collapses to the Boolean Hierarchy. (iii) S_21 proves NPP/poly iff S21 proves coNPNP/O(log n). (iv) If S_21 proves NPP/poly then S21 proves that the Polynomial Hierarchy collapses to PNP[log n]. (v) If S22 proves NPP/poly then S22 proves that the Polynomial Hierarchy collapses to PNP. Motivated by these results we introduce a new concept in proof complexity: proof systems with advice, and we make some initial observations about them.

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Stephen Cook. Jan Krajíček. "Consequences of the provability of NPP/poly." J. Symbolic Logic 72 (4) 1353 - 1371, December 2007. https://doi.org/10.2178/jsl/1203350791

Information

Published: December 2007
First available in Project Euclid: 18 February 2008

zbMATH: 1133.03035
MathSciNet: MR2371210
Digital Object Identifier: 10.2178/jsl/1203350791

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 4 • December 2007
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