Boolean Satisfiability using Noise Based Logic

TL;DR

This paper introduces a deterministic noise-based logic (NBL) algorithm for solving the Boolean SAT problem, leveraging superposition to determine satisfiability efficiently, with potential hardware implementations discussed.

Contribution

It presents the first NBL-based SAT algorithm that uses superposition to check satisfiability in a single step, offering a novel approach to solving SAT problems.

Findings

NBL allows superposition of input vectors for SAT instances.

The algorithm can determine satisfiability in a single operation.

Simulations validate the approach's effectiveness.

Abstract

In this paper, we present a novel algorithm to solve the Boolean Satisfiability (SAT) problem, using noise-based logic (NBL). Contrary to what the name may suggest, NBL is not a random/fuzzy logic system. In fact, it is a completely deterministic logic system. A key property of NBL is that it allows us to apply a superposition of many input vectors to a SAT instance at the same time, circumventing a key restriction and assumption in the traditional approach to solving SAT. By exploiting the superposition property of NBL, our NBL-based SAT algorithm can determine whether an instance is SAT or not in a single operation. A satisfying solution can be found by iteratively performing SAT check operations up to n times, where n is the number of variables in the SAT instance. Although this paper does not focus on the realization of an NBL-based SAT engine, such an engine can be conceived using analog circuits (wide-band amplifiers, adders and multipliers), FPGAs or ASICs. Additionally, we also discus scalability of our approach, which can apply to NBL in general. The NBL-based SAT engine described in this paper has been simulated in software for validation purposes.