Bounding Laconic Proof Systems by Solving CSPs in Parallel

Abstract

We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that \MIPone[k,c,s] \subseteq \PSPACE provided s/c \leq (.62-o(1))k/2^k, resolving a question of Austrin, H\aa stad, and Pass. Here \MIPone[k,c,s] is the class of languages decidable with completeness c and soundness s by an interactive proof system with k provers, each constrained to communicate just 1 bit.