Self-averaging of digital memcomputing machines

TL;DR

Digital memcomputing machines (DMMs) are a novel class of physics-inspired computational systems that efficiently solve combinatorial problems, exhibiting self-averaging behavior in solution times that enhances robustness and insensitivity to problem details.

Contribution

The paper demonstrates that DMMs' solution times follow an inverse Gaussian distribution and self-average with increasing problem size, supported by analytical and numerical evidence.

Findings

Solution times follow an inverse Gaussian distribution.

DMMs' solution times self-average as problem size increases.

DMMs are more robust to problem variations than traditional algorithms.

Abstract

Digital memcomputing machines (DMMs) are a new class of computing machines that employ non-quantum dynamical systems with memory to solve combinatorial optimization problems. Here, we show that the time to solution (TTS) of DMMs follows an inverse Gaussian distribution, with the TTS self-averaging with increasing problem size, irrespective of the problem they solve. We provide both an analytical understanding of this phenomenon and numerical evidence by solving instances of the 3-SAT (satisfiability) problem. The self-averaging property of DMMs with problem size implies that they are increasingly insensitive to the detailed features of the instances they solve. This is in sharp contrast to traditional algorithms applied to the same problems, illustrating another advantage of this physics-based approach to computation.