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.

翻译：数字忆阻计算系统是一种新型计算系统，它利用非量子动力学系统结合记忆机制来解决组合优化问题。本文证明，数字忆阻计算系统的求解时间服从逆高斯分布，且该求解时间随问题规模增大呈现自平均特性，与所求解的具体问题类型无关。我们通过解析推导和数值实验（求解3-SAT可满足性问题的实例）两方面验证了这一现象。数字忆阻计算系统随问题规模增大而表现出的自平均性意味着，它们对求解实例的细节特征越来越不敏感。这与传统算法在处理相同问题时的表现形成鲜明对比，进一步体现了这种基于物理的计算方法的优势。