k-SAT Is No Harder Than Decision-Unique-k-SAT

  • Chris Calabro
  • Ramamohan Paturi
Conference paper

DOI: 10.1007/978-3-642-03351-3_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5675)
Cite this paper as:
Calabro C., Paturi R. (2009) k-SAT Is No Harder Than Decision-Unique-k-SAT. In: Frid A., Morozov A., Rybalchenko A., Wagner K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg

Abstract

We resolve an open question by [3]: the exponential complexity of deciding whether a k-CNF has a solution is the same as that of deciding whether it has exactly one solution, both when it is promised and when it is not promised that the input formula has a solution. We also show that this has the same exponential complexity as deciding whether a given variable is backbone (i.e. forced to a particular value), given the promise that there is a solution. We show similar results for True Quantified Boolean Formulas in k-CNF, k-Hitting Set (and therefore Vertex Cover), k-Hypergraph Independent Set (and therefore Independent Set), Max-k-SAT, Min-k-SAT, and 0-1 Integer Programming with inequalities and k-wide constraints.

Keywords

k-SAT unique satisfiability exponential complexity quantified Boolean formulas hitting set independent set 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Chris Calabro
    • 1
  • Ramamohan Paturi
    • 1
  1. 1.University of California, San DiegoLa JollaUSA

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