Non-signaling proofs with o(√ log n) provers are in PSPACE

Non-signaling proofs, motivated by quantum computation, have found applications in cryptography and hardness of approximation. An important open problem is characterizing the power of non-signaling proofs. It is known that non-signaling proofs with two provers are characterized by PSPACE and that non-signaling proofs with poly(n)-provers are characterized by EXP. However, the power of k-prover non-signaling proofs, for 2<k<(n) remained an open problem.