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Limitations of Restricted Branching in Clause Learning

  • Matti Järvisalo
  • Tommi Junttila
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4741)

Abstract

The techniques for making decisions, i.e., branching, play a central role in complete methods for solving structured CSP instances. In practice, there are cases when SAT solvers benefit from limiting the set of variables the solver is allowed to branch on to so called input variables. Theoretically, however, restricting branching to input variables implies a super-polynomial increase in the length of the optimal proofs for DPLL (without clause learning), and thus input-restricted DPLL cannot polynomially simulate DPLL. In this paper we settle the case of DPLL with clause learning. Surprisingly, even with unlimited restarts, input-restricted clause learning DPLL cannot simulate DPLL (even without clause learning). The opposite also holds, and hence DPLL and input-restricted clause learning DPLL are polynomially incomparable. Additionally, we analyse the effect of input-restricted branching on clause learning solvers in practice with various structural real-world benchmarks.

Keywords

Proof System Linear Temporal Logic Conjunctive Normal Form Truth Assignment Boolean Circuit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Matti Järvisalo
    • 1
  • Tommi Junttila
    • 1
  1. 1.Helsinki University of Technology (TKK), Laboratory for Theoretical Computer Science, P.O. Box 5400, FI-02015 TKKFinland

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