Exponential lower bounds for DPLL algorithms on satisfiable random 3-CNF formulas

  • Authors:

  • Dimitris Achlioptas;Ricardo Menchaca-Mendez

  • Affiliations:

  • University of Athens, Greece, CTI, Greece, University of California, Santa Cruz;University of California, Santa Cruz

  • Venue:
  • SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
  • Year:
  • 2012

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Abstract

We consider the performance of a number of DPLL algorithms on random 3-CNF formulas with n variables and m=rn clauses. A long series of papers analyzing so-called "myopic" DPLL algorithms has provided a sequence of lower bounds for their satisfiability threshold. Indeed, for each myopic algorithm ${\mathcal A}$ it is known that there exists an algorithm-specific clause-density, $r_{\mathcal A}$, such that if $r exponential time. Specifically, all extensions of orderred-dll take exponential time for r2.78 and the same is true for generalized unit clause for all r3.1. Our results imply exponential lower bounds for many other myopic algorithms for densities similarly close to the corresponding $r_{\mathcal A}$.