Off the Trail: Re-examining the CDCL Algorithm

Abstract

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.

A Duality-Aware Calculus for Quantified Boolean Formulas

“…Our strategy requires to stop propagation as soon as a leaf is reached (which in turn is required for learning to be applied). In SAT it has been considered to lift this requirement, which however requires additional care during learning [15]. It is unclear at this point whether this also applies to our calculus or QBF.…”

Satsisfiability and Systematicity

“…These algorithms are very different in spirit from the ones that we have described thus far, working with complete variable assignments and using hill climbing to attempt to gradually convert these assignments to solutions of the problems being investigated. While competitive in the 1990's, the progress on systematic algorithms has been such that these fundamentally nonsystematic approaches are currently given relatively little attention, although recent work has shown that the connection between these algorithms and the cdcl approach is closer than one might think (Goultiaeva & Bacchus, 2012).…”