A Multilevel Approach Applied to Sat-Encoded Problems

Abstract

The satisfiability problem (SAT) which is known to be NP-complete (7) plays a central role problem in many applications in the fields of VLSI Computer-Aided design, Computing Theory, and Artificial Intelligence. Generally, a SAT problem is defined as follows. A propositional formula Φ = ∧m j=1 Cj with m clauses and n Boolean variables is given. Each Boolean variable, xi, i ∈ {1, . . . , n}, takes one of the two values, True or False. A clause , in turn, is a disjunction of literals and a literal is a variable or its negation. Each clause Cj has the form: