Solving Boolean Satisfiability Problems Using A Hypergraph-based Probabilistic Computer

TL;DR

This paper introduces a hypergraph-based probabilistic computing approach for solving 3-SAT problems, significantly reducing complexity and increasing success rates compared to traditional methods.

Contribution

It presents a novel direct mapping technique that transforms 3-SAT problems into hypergraph structures, bypassing traditional logic synthesis.

Findings

Vertex count reduced from 112 to 20 for uf20-01 instance

Success rate increased to 99% with the new method

Framework extendable to k-SAT problems

Abstract

Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex logic synthesis steps. In this work, we present a novel approach for solving the 3-SAT Boolean satisfiability problem using hypergraph-based probabilistic computers obtained through direct mapping. This method directly translates 3-SAT logical expressions into hypergraph structures, thereby circumventing conventional logic decomposition and synthesis procedures, and offering a more streamlined solver architecture. For a uf20-01 instance, our approach significantly reduces the vertex number from 112 to 20 with a reduced solution space from 2112 to 220. Numerical simulations demonstrate that the proposed hypergraph-based solver achieves a significantly higher success rate of up to 99%, compared to merely 1% for conventional solvers. Furthermore, the proposed direct mapping method can be extended to solve k-SAT problems, which provides a scalable framework for tackling more complex satisfiability problems using probabilistic computing in the future.