Accurate modeling of continuous-time SAT solvers in SPICE

TL;DR

This paper develops and tests accurate SPICE circuit models of continuous-time dynamical systems for solving SAT problems, enabling detailed simulation and analysis of analog and digital memcomputing approaches.

Contribution

It introduces advanced numerical integration implementations of analog SAT and digital memcomputing solvers in SPICE, with Python scripts converting SAT problems into circuit netlists for simulation.

Findings

Successful simulation of analog SAT and digital memcomputing in SPICE

Insights into the behavior of continuous-time solvers from circuit simulations

Potential applications of continuous-time networks beyond SAT solving

Abstract

Recently, there has been an increasing interest in employing dynamical systems as solvers of NP-complete problems. In this paper, we present accurate implementations of two continuous-time dynamical solvers, known in the literature as analog SAT and digital memcomputing, using advanced numerical integration algorithms of SPICE circuit simulators. For this purpose, we have developed Python scripts that convert Boolean satisfiability (SAT) problems into electronic circuits representing the analog SAT and digital memcomputing dynamical systems. Our Python scripts process conjunctive normal form (CNF) files and create netlists that can be directly imported into LTspice. We explore the SPICE implementations of analog SAT and digital memcomputing solvers by applying these to a selected set of problems and present some interesting and potentially useful findings related to digital memcomputing and analog SAT. In this work, we also introduce networks of continuous-time solvers with potential applications extending beyond the solution of Boolean satisfiability problems.