Abstract

The ability to reduce either the number of variables or clauses in instances of the Propositional Satisfiability problem (SAT) is expected to impact the computational effort of solving a given instance. Moreover, the ability to infer new clauses is also expected to impact the computational effort of SAT solvers. Even though new clauses are inferred and added to the formula, the task of solving a target problem instance can become significantly simplified. The main objectives of this paper are to review existing simplification techniques for formulas in Conjunctive Normal Form (CNF), and to evaluate the effectiveness of the different simplification techniques, based on existing propositional simplifiers and state-of-the-art SAT solvers. Experimental results, obtained on representative hard real-world problem instances, indicate that simplification can play a puzzling role in Propositional Satisfiability. The main experimental conclusion is that reducing the number of variables or inferring additional clauses is not necessarily useful in terms of reducing the amount of search performed by backtrack search SAT algorithms, but that depends on which simplification techniques are actually used.

Citations