Off the Trail: Re-examining the CDCL Algorithm

Abstract

Most state of the art SAT solvers for industrial problems are based on the Conflict Driven Clause Learning (CDCL) paradigm. Although this paradigm evolved from the systematic DPLL search algorithm, modern techniques of far backtracking and restarts make CDCL solvers non-systematic. CDCL solvers do not systematically examine all possible truth assignments as does DPLL. Local search solvers are also non-systematic and in this paper we show that CDCL can be reformulated as a local search algorithm: a local search algorithm that through clause learning is able to prove UNSAT. We show that the standard formulation of CDCL as a backtracking search algorithm and our new formulation of CDCL as a local search algorithm are equivalent, up to tie breaking. In the new formulation of CDCL as local search, the trail no longer plays a central role in the algorithm. Instead, the ordering of the literals on the trail is only a mechanism for efficiently controlling clause learning. This changes the paradigm and opens up avenues for further research and algorithm design. For example, in QBF the quantifier places restrictions on the ordering of variables on the trail. By making the trail less important, an extension of our local search algorithm to QBF may provide a way of reducing the impact of these variable ordering restrictions.