Formulating Oscillator-Inspired Dynamical Systems to Solve Boolean Satisfiability

TL;DR

This paper introduces two oscillator-inspired dynamical systems designed to solve complex Boolean satisfiability problems, leveraging energy minimization principles for potentially more efficient computation.

Contribution

It formulates novel dynamical systems inspired by oscillators to solve 3-SAT and Max-NAE-3-SAT problems, advancing physics-inspired computing approaches.

Findings

Successfully maps 3-SAT solutions to system dynamics.

Demonstrates solution mapping for Max-NAE-3-SAT.

Provides a new framework for oscillator-based problem solving.

Abstract

Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many of which are still challenging to solve using conventional digital solvers. In this work, we formulate two oscillator-inspired dynamical systems to solve quintessential computationally intractable problems in Boolean satisfiability (SAT). The system dynamics are engineered such that they facilitate solutions to two different flavors of the SAT problem. We formulate the first dynamical system to compute the solution to the 3-SAT problem, while for the second system, we show that its dynamics map to the solution of the Max-NAE-3-SAT problem. Our work advances understanding of how this physics-inspired approach can be used to address challenging problems in computing.