A neural network approach to the 3-satisfiability problem

Abstract

A circuit is described for which the interconnections may be established to reflect a particular instance of the 3-Satisfiability problem. Analysis of the circuit reveals that it can proceed from an unbiased starting state to a stable state which can be interpreted as a satisfying truth value assignment for the 3-Satisfiability problem, if such an assignment exists. This stable configuration represents the global minimum of an energy function. While no analytic evidence is presented to guarantee that the trajectory does not become trapped in a local minimum, supporting empirical evidence is cited which indicates that it does not. Finally, it is shown that the network scales polynomially with respect to the size of the 3-Satisfiability problem both in circuit hardware and in convergence time. The relevance of this phenomenon to the P = NP question is discussed.