Solving NP-complete problems with delayed signals: an overview of current research directions

TL;DR

This paper reviews current research on unconventional computing devices that use delayed signals to solve NP-complete problems, discussing principles, components, and experimental problem-solving successes.

Contribution

It provides an overview of the principles, components, and physical implementations of delayed signal-based computing devices for NP-complete problems, highlighting recent problem-solving achievements.

Findings

Six NP-complete problems solved using delayed signals

Various physical signals (light, electric, sound) employed in implementations

Insights into properties and precision requirements of signals

Abstract

In this paper we summarize the existing principles for building unconventional computing devices that involve delayed signals for encoding solutions to NP-complete problems. We are interested in the following aspects: the properties of the signal, the operations performed within the devices, some components required for the physical implementation, precision required for correctly reading the solution and the decrease in the signal's strength. Six problems have been solved so far by using the above enumerated principles: Hamiltonian path, travelling salesman, bounded and unbounded subset sum, Diophantine equations and exact cover. For the hardware implementation several types of signals can be used: light, electric power, sound, electro-magnetic etc.