Dependent and Independent Variables in Propositional Satisfiability

Propositional reasoning (SAT) is central in many applications of Computer Science. Several decision procedures for SAT have been proposed, along with optimizations and heuristics to speed them up. Currently, the most effective implementations are based on the Davis, Logemann, Loveland method. In this method, the input formula is represented as a set of clauses, and the space of truth assignments is searched by iteratively assigning a literal until all the clauses are satisfied, or a clause is violated and backtracking occurs. Once a new literal is assigned, pruning techniques (e.g., unit propagation) are used to cut the search space by inferring truth values for other variables.In this paper, we investigate the "independent variable selection (IVS) heuristic", i.e., given a formula on the set of variables N, the selection is restricted to a - possibly small - subset S which is sufficient to determine a truth value for all the variables in N. During the search phase, scoring and selection of the literal to assign next are restricted to S, and the truth values for the remaining variables are determined by the pruning techniques of the solver. We discuss the possible advantages and disadvantages of the IVS heuristic. Our experimental analysis shows that obtaining either positive or negative results strictly depends on the type of problems considered, on the underlying scoring and selection technique, and also on the backtracking scheme.

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