Complexity of Homogeneous Co-Boolean Constraint Satisfaction Problems

TL;DR

This paper establishes a dichotomy theorem for the complexity of CSPs over finite domains built on graphs of homogeneous co-Boolean functions, clarifying the boundary between tractable and intractable cases.

Contribution

It introduces a dichotomy theorem specifically for CSPs over graphs of homogeneous co-Boolean functions, expanding understanding of their computational complexity.

Findings

Dichotomy theorem for CSPs with homogeneous co-Boolean functions

Classification of problems into tractable and intractable cases

Extension of complexity results to a specific class of unary functions

Abstract

Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NP-complete, but its complexity depends on a template, usually a set of relations, upon which they are constructed. Following this template, there exist tractable and intractable instances of CSPs. It has been proved that for each CSP problem over a given set of relations there exists a corresponding CSP problem over graphs of unary functions belonging to the same complexity class. In this short note we show a dichotomy theorem for every finite domain D of CSP built upon graphs of homogeneous co-Boolean functions, i.e., unary functions sharing the Boolean range {0, 1}.