Parallel cooperative propositional theorem proving

  • Authors:

  • Fumiaki Okushi

  • Affiliations:

  • Computer Science Department, 225 AS, University of California, Santa Cruz, CA 95064, USA E-mail: okushi@cs.ucsc.edu

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 1999

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Abstract

A parallel satisfiability testing algorithm called Parallel Modoc is presented. Parallel Modoc is based on Modoc, which is based on propositional Model Elimination with an added capability to prune away certain branches that cannot lead to a successful subrefutation. The pruning information is encoded in a partial truth assignment called an autarky. Parallel Modoc executes multiple instances of Modoc as separate processes and allows processes to cooperate by sharing lemmas and autarkies as they are found. When a Modoc process finds a new autarky or a new lemma, it makes the information available to other Modoc processes via a “blackboard”. Combining autarkies generally is not straightforward because two autarkies found by two separate processes may have conflicting assignments. The paper presents an algorithm to combine two arbitrary autarkies to form a larger autarky. Experimental results show that for many of the formulas, Parallel Modoc achieves speedup greater than the number of processors. Formulas that could not be solved in an hour by Modoc were often solved by Parallel Modoc in the order of minutes and, in some cases, in seconds.