Acceleration of digital memcomputing by jumps

TL;DR

This paper explores how incorporating jumps into digital memcomputing machines enhances their speed and efficiency in solving complex optimization problems, with potential improvements up to 75%.

Contribution

It introduces a novel jump mechanism into DMMs, demonstrating significant speedups in solving SAT problems compared to traditional DMMs.

Findings

Jumps can improve solving times by up to 75%.

Jumps modify scaling exponents in DMMs.

Large jumps make voltage variables behave almost binary.

Abstract

In this article, we present the potential benefits of incorporating jumps into the dynamics of digital memcomputing machines (DMMs), which have been developed to address complex optimization problems. We illustrate the potential speed improvement of a DMM solver with jumps over an unmodified DMM solver by solving Boolean satisfiability (SAT) problems of different complicatedness. Our findings suggest that jumps can modify scaling exponents and improve solving times by up to 75 %. Interestingly, the advantages of jumps can be seen in cases where the size of the jump is so large that otherwise the continuous dynamics of voltage variables becomes almost binary.