A Dichotomy Theorem for Typed Constraint Satisfaction Problems

摘要

This paper is a contribution to the general investigation into how the complexity of constraint satisfaction problems (CSPs) is determined by the form of the constraints. Schaefer proved that the Boolean generalized CSP has the dichotomy property (i.e., all instances are either in P or are NP-complete), and gave a complete and simple classification of those instances which are in P (assuming P ≠ NP). In this paper we consider a special subcase of the generalized CSP. For this CSP subcase, we require that the variables be drawn from disjoint Boolean domains. Our relation set contains only two elements: a monotone multiple-arity Boolean relation R and its complement R. We prove a dichotomy theorem for these monotone function CSPs, and characterize those monotone functions such that the corresponding problem resides in P.