论文信息 - Proving SAT does not have small circuits with an application to the two queries problem

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 if P/sup NP[1]/=P/sup NP[2]/, then the polynomial-time hierarchy collapses to S/sub 2//sup P//spl sube//spl Sigma//sub 2//sup p//spl cap//spl Pi//sub 2//sup p/. Even showing that the hierarchy collapsed to /spl Sigma//sub 2//sup p/ remained open.

Lance Fortnow | Aduri Pavan | Samik Sengupta

[1] Sampath Kannan,et al. Oracles and Queries That Are Sufficient for Exact Learning , 1996, J. Comput. Syst. Sci..

[2] Ran Canetti. More on BPP and the Polynomial-Time Hierarchy , 1996, Inf. Process. Lett..

[3] Mitsunori Ogihara,et al. A relationship between difference hierarchies and relativized polynomial hierarchies , 2005, Mathematical systems theory.

[4] Oded Goldreich,et al. Foundations of Cryptography: List of Figures , 2001 .

[5] Oded Goldreich. Foundations of Cryptography: Index , 2001 .

[6] Leslie G. Valiant,et al. Random Generation of Combinatorial Structures from a Uniform Distribution , 1986, Theor. Comput. Sci..

[7] Klaus W. Wagner,et al. On boolean lowness and boolean highness , 2001, Theor. Comput. Sci..

[8] Jim Kadin. The Polynomial Time Hierarchy Collapses if the Boolean Hierarchy Collapses , 1988, SIAM J. Comput..

[9] Richard Chang,et al. The Boolean Hierarchy and the Polynomial Hierarchy: A Closer Connection , 1996, SIAM J. Comput..

[10] Lance Fortnow,et al. Two Queries , 1999, J. Comput. Syst. Sci..

[11] Alexander Russell,et al. Symmetric alternation captures BPP , 1998, computational complexity.

[12] Mark W. Krentel. The Complexity of Optimization Problems , 1986, Computational Complexity Conference.