Constant unary constraints and symmetric real-weighted counting CSPs

Abstract

In a discussion on the computational complexity of approximately solving Boolean counting constraint satisfaction problems (or #CSPs), we demonstrate the approximability of two constant unary constraints by an arbitrary nonempty set of real-valued constraints. A use of auxiliary free unary constraints has proven to be useful in establishing a complete classification of weighted #CSPs. Using our approximability result, we can clarify the role of such auxiliary free unary constraints by constructing approximation-preserving reductions from #SAT to #CSPs with symmetric real-valued constraints of arbitrary arities. © Springer-Verlag 2012.