Accurate modeling of continuous-time SAT solvers in SPICE

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.