Journal of Symbolic Logic

Consequences of the provability of NPP/poly

Stephen Cook and Jan Krajíček

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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.

Article information

Source
J. Symbolic Logic Volume 72, Issue 4 (2007), 1353-1371.

Dates
First available in Project Euclid: 18 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1203350791

Digital Object Identifier
doi:10.2178/jsl/1203350791

Mathematical Reviews number (MathSciNet)
MR2371210

Zentralblatt MATH identifier
1133.03035

Citation

Cook, Stephen; Krajíček, Jan. Consequences of the provability of NP ⊆ P/poly . J. Symbolic Logic 72 (2007), no. 4, 1353--1371. doi:10.2178/jsl/1203350791. https://projecteuclid.org/euclid.jsl/1203350791.


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