Towards a Physical Oracle for the Partition Problem using Analogue Computing

Abstract

Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of work relies on Turing machines or equivalent models, all of which relate to digital computing. This raises the question of whether a computer that is (partly) non-digital could offer a new door towards an efficient solution. And indeed, the partition problem, which is another NP-complete sibling of the famous Boolean satisfiability problem SAT, might be open to efficient solutions using analogue computing. We investigate this hypothesis here, providing experimental evidence that Partition, and in turn also SAT, may become tractable on a combined digital and analogue computing machine. This work provides mostly theoretical and based on simulations, and as such does not exhibit a polynomial time algorithm to solve NP-complete problems. Instead, it is intended as a pointer to new directions of research on special-purpose computing architectures that may help handling the class NP efficiently.