On SAT01 Problem

We introduce a new NP-complete problem, which is denoted SAT01. It has some special properties, which give us an opportunity to speculate about a particular place of the problem in the class NP. The first reason of this is that many different from each other NP problems can be reduced to SAT01 very easily and the new introduced SAT01 variables have natural meanings at that. The second reason is that a powerful propagation method for SAT01 is constructed to perform its reduction and to recognize hidden binary relations among variables. After all, since the problem is formulated as a system of linear equations and inequalities for binary variables we are able to use heuristics based on solving of the real relaxation of its constraints. Due to all these properties we have solved many hard instances of different NP problems with good performance. 1 Definition of SAT01 Problem SAT01 is a generalization of the well-known set partition problem (SPP) [1] in the non-optimization form..