Universal Memcomputing Machines

TL;DR

This paper introduces universal memcomputing machines (UMMs), a brain-inspired computing paradigm with memory-based processing that can solve complex problems efficiently, potentially revolutionizing computational architecture.

Contribution

The paper formally defines UMMs, proves their Turing-completeness and NP-complete problem-solving capability in polynomial time, and demonstrates a hardware implementation example.

Findings

UMMs are Turing-complete and can solve NP-complete problems in polynomial time.

They exhibit intrinsic parallelism, functional polymorphism, and exponential data compression.

A hardware prototype for subset-sum problem demonstrates practical feasibility.

Abstract

We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location. We analytically prove that the memory properties of UMMs endow them with universal computing power - they are Turing-complete -, intrinsic parallelism, functional polymorphism, and information overhead, namely their collective states can support exponential data compression directly in memory. We also demonstrate that a UMM has the same computational power as a non-deterministic Turing machine, namely it can solve NP--complete problems in polynomial time. However, by virtue of its information overhead, a UMM needs only an amount of memory cells (memprocessors) that grows polynomially with the problem size. As an example we provide the polynomial-time solution of the subset-sum problem and a simple hardware implementation of the same. Even though these results do not prove the statement NP=P within the Turing paradigm, the practical realization of these UMMs would represent a paradigm shift from present von Neumann architectures bringing us closer to brain-like neural computation.