The Complexity of Counting CSPd

Counting CSPd is the counting constraint satisfaction problem (# CSP in short) restricted to the instances where every variable occurs a multiple of d times. This paper revisits tractable structures in # CSP and gives a complexity classification theorem for # CSPd with algebraic complex weights. The result unifies affine functions (stabilizer states in quantum information theory) and related variants such as the local affine functions, the...