WSAT Dynamics and Density of States

Abstract

This paper undertakes the study of the well-known SAT problem using d.o.s. It shows through Satisfiability benchmark instances that d.o.s follows in good approximation a normal law. Information given by d.o.s turns out to be very informative to explain and predict the dynamics of local search methods. Thus, it allows us to obtain some explanations of an intriguing behavior of the local search method WSAT. Indeed, our experiments show that WSAT stagnates invariably within a particular cost interval, independently of the starting assignment. This behavior can be explained using d.o.s. The article is organized as follows. Section 2 presents an intriguing experiment with WSAT. Section 3, defines d.o.s. Section 4 measures d.o.s for various SAT instances and shows its relation with WSAT dynamics. Section 6 concludes and gives some further direction