On Moderately Exponential Time for SAT

  • Evgeny Dantsin
  • Alexander Wolpert
Conference paper

DOI: 10.1007/978-3-642-14186-7_27

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6175)
Cite this paper as:
Dantsin E., Wolpert A. (2010) On Moderately Exponential Time for SAT. In: Strichman O., Szeider S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg

Abstract

Can sat be solved in “moderately exponential” time, i.e., in time p(|F|) 2cn for some polynomial p and some constant c < 1, where F is a CNF formula of size |F| over n variables? This challenging question is far from being resolved. In this paper, we relate the question of moderately exponential complexity of sat to the question of moderately exponential complexity of problems defined by existential second-order sentences. Namely, we extend the class SNP (Strict NP) that consists of Boolean queries defined by existential second-order sentences where the first-order part has a universal prefix. The extension is obtained by allowing a ∀ ... ∀ ∃ ... ∃ prefix in the first-order part. We prove that if sat can be solved in moderately exponential time then all problems in the extended class can also be solved in moderately exponential time.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Evgeny Dantsin
    • 1
  • Alexander Wolpert
    • 1
  1. 1.Department of Computer ScienceRoosevelt UniversityChicagoUSA

Personalised recommendations