Resolvent Clause Weighting Local Search

Abstract

Considerable progress in local search has recently been made in using clause weighting algorithms to solve satisfiability benchmark problems. While these algorithms have outperformed earlier stochastic techniques on many larger problems, this improvement has generally required extra, problem specific, parameters requiring fine tuning to problem domains for optimal run-time performance. In a previous paper, the use of parameters, specifically in relation to the DLM clause weighting algorithm, was examined to identify underlying features in clause weighting that could be used to eliminate or predict workable parameter settings. A simplified clause weighting algorithm, Maxage, based on DLM, was proposed that reduced the DLMs run-time parameters to a single parameter. This paper presents an algorithm, RLS, based on DLM and Maxage, which combines the use of resolvent clauses with clause weighting. In RLS, clause resolvents that contain fewer literals than their parent clauses become active in the SAT problem whenever a parent clause is false and a clause weight increase is performed. This technique reduces the overhead of resolvent clauses and also adds extra information for the local search when it is required. In this paper RLS is compared with the state of the art DLM and SAPS clause weighting local search algorithms.