A Continuous-time Dynamical System Solving the Satisfiability Problem

Abstract

The Boolean satisfiability (SAT) problem, which is a problem of finding a satisfying assignment of given Boolean formulae, is an important problem both in theory and practice. In this article, the dynamical system solving the SAT problem proposed by Ercsey-Ravasz and Toroczkai is described. This system reduces the SAT problem as the time-varying optimization problem and solves it using the gradient descent method in continuous time and state space. It has interesting dynamical properties, such as transient chaos, and also has possible application as electric circuit implementation.