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2010
ACM

Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses

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Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses
Consider the following two-player communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small cost, where the cost measure is the number of bits of communication from the first player to the second player. For any integer d 3 and positive real we show that if satisfiability for n-variable dCNF formulas has a protocol of cost O(nd) then coNP is in NP/poly, which implies that the polynomial-time hierarchy collapses to its third level. The result even holds when the first player is conondeterministic, and is tight as there exists a trivial protocol for = 0. Under the hypothesis that coNP is not in NP/poly, our result implies tight lower bounds for parameters of interest in several areas, namely sparsification, kernelization in parameterized complexity, lossy compression, and probab...
Holger Dell and Dieter van Melkebeek
Added 09 Aug 2010
Updated 09 Aug 2010
Type Conference
Year 2010
Where STOC
Authors Holger Dell and Dieter van Melkebeek
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