Solving the Satisfiability Problem through Boolean Networks

$EVWUDFW. In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN fixed points correspond to the SAT solutions. The mapping presented allows to develop a new class of algorithms to solve SAT. Moreover, this new approach suggests new ways to combine symbolic and connectionist computation and provides a general framework for local search algorithms. The satisfiability problem (SAT) [Garey and Johnson, 1979] has an important role in computer science and it has been widely investigated. The SAT problem is a NP-complete problem concerning the satisfiability of boolean formulas, i.e., find an assignment of boolean values to variables such that the formula is satisfied. SAT is very important in several Artificial Intelligence areas, like propositional calculus, constraints satisfaction and planning. For its theoretical and practical relevance, many specialized (complete and incomplete) algorithms have been developed. We present a novel approach to solve SAT, based on Boolean Networks (BN). Up to this time, boolean networks have been used for modeling complex adaptive systems [Cowan HW DO 1994], and in the field of machine learning (see for instance [Dorigo, 1994]). In this approach, we map a SAT instance in a BN, and we simulate its dynamics; the stationary states of the net correspond to the solutions of SAT. Due to the BN structure and dynamics used, the resulting algorithms are incomplete. We have developed and tested three algorithms, each of them is derived from a variant of boolean networks: synchronous, probabilistic and asynchronous boolean nets. The first algorithm has led to disappointing results, while the second and the third had performed better. The new approach represents a bind between symbolic and connectionist computation , and it allows to develop new algorithms to solve SAT. This work represents a first investigation on the subject and it mainly refers to the founding principles. The algorithms presented are based on elementary dynamics of boolean networks, without using any heuristic function to guide the search, nor optimization criteria.