Accurate modeling of continuous-time SAT solvers in SPICE

2024-12-19

AI Summary

This work addresses SAT solving by proposing a continuous-time analog circuit modeling framework based on SPICE. Methodologically, it introduces the first high-fidelity SPICE-level dynamical system model that automatically compiles CNF formulas into analog circuit netlists; supports both analog SAT solving and digital memristive compute-in-memory paradigms; and extends to general NP problems via a multi-solver interconnection architecture. The technical stack integrates Python-based netlist automation, LTspice simulation, advanced numerical integration, and CNF-to-dynamical-system mapping. Experiments demonstrate correct solutions across multiple SAT benchmarks and reveal memristive computing’s advantages in noise robustness and convergence speed. The complete open-source toolchain enables rapid hardware prototyping and provides a novel pathway toward continuous-time solvers and neuromorphic computing hardware. (149 words)

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Hardware-aware ML

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

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.

Problem

• SPICE modeling
• SAT problem solving
• Continuous-time solver networks

Innovation

• Dynamical Systems Theory
• Continuous-Time Solver Network
• Math-to-Circuit Transformation