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Parameterized and Subexponential-Time Complexity of Satisfiability Problems and Applications

  • Iyad Kanj
  • Stefan Szeider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8881)

Abstract

We study the parameterized and the subexponential-time complexity of the weighted and unweighted satisfiability problems on bounded-depth Boolean circuits. We establish relations between the subexponential-time complexity of the weighted and unweighted satisfiability problems, and use them to derive relations among the subexponential-time complexity of several \(\text {NP}\)-hard problem. For instance, we show that the weighted monotone satisfiability problem is solvable in subexponential time if and only if CNF-Sat is. The aforementioned result implies, via standard reductions, that several \(\text {NP}\)-hard problems are solvable in subexponential time if and only if CNF-Sat is. We also obtain threshold functions on structural circuit parameters including depth, number of gates, and fan-in, that lead to tight characterizations of the parameterized and the subexponential-time complexity of the circuit problems under consideration. For instance, we show that the weighted satisfiability problem is \(\text {FPT}\) on bounded-depth circuits with \(O(\log {n})\) gates, where \(n\) is the number of variables in the circuit, and is not \(\text {FPT}\) on bounded-depth circuits of \(\omega (\log {n})\) gates unless the Exponential Time Hypothesis (ETH) fails.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of ComputingDePaul UniversityChicagoUSA
  2. 2.Vienna University of TechnologyViennaAustria

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