Proving SAT does not have Small Circuits with an Application to the Two

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http://doi.ieeecomputersociety.org/10.1109/CCC.2003.1214433

18th Annual IEEE Conference on Comput ...

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	Lance Fortnow, A. Pavan, Samik Sengupta, "Proving SAT does not have Small Circuits with an Application to the Two," Computational Complexity, Annual IEEE Conference on, pp. 347, 18th Annual IEEE Conference on Computational Complexity (CCC'03), 2003.

	BibTex	x
	@article{ 10.1109/CCC.2003.1214433, author = {Lance Fortnow and A. Pavan and Samik Sengupta}, title = {Proving SAT does not have Small Circuits with an Application to the Two}, journal ={Computational Complexity, Annual IEEE Conference on}, volume = {0}, year = {2003}, issn = {1093-0159}, pages = {347}, doi = {http://doi.ieeecomputersociety.org/10.1109/CCC.2003.1214433}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - CONF JO - Computational Complexity, Annual IEEE Conference on TI - Proving SAT does not have Small Circuits with an Application to the Two SN - 1093-0159 SP EP A1 - Lance Fortnow, A1 - A. Pavan, A1 - Samik Sengupta, PY - 2003 KW - null VL - 0 JA - Computational Complexity, Annual IEEE Conference on ER -

Lance Fortnow

A. Pavan

Samik Sengupta

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_{}^{NP} [1] = P_{}^{NP[2]}, then the polynomial-time hierarchy collapses to S_2^P \subseteq \sum {} _2^P \cap \prod {} _2^P Even showing that the hierarchy collapsed to \sum {} _2^P remained open prior to this paper.

Citation:

Lance Fortnow, A. Pavan, Samik Sengupta, "Proving SAT does not have Small Circuits with an Application to the Two," ccc, pp.347, 18th Annual IEEE Conference on Computational Complexity (CCC'03), 2003

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