In Some Curved Spaces, One Can Solve NP-Hard Problems in Polynomial Time

Abstract

Abstract In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NP-hard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved spaces. 1 Introduction and Formulation of the Problem Many practical problems are NP-hard. It is well known that many im-portant practical problems are NP-hard; see, e.g., [11, 14, 27]. Under the usual hypothesis that P6=NP, NP-hardness has the following intuitive meaning: everyalgorithm which solves all instances of the corresponding problem requires, for some instances, non-realistic hyper-polynomial (probably exponential) time ona Turing machine (and thus, on most known computational devices)