Non-signaling proofs with O (p√logn) provers are in PSPACE

Abstract

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 0), then the corresponding 2-prover game has value less than 1 - 2dk2 (for some constant d>0). In the second route we show that the value of a sub-non-signaling game can be approximated in space that is polynomial in the communication complexity and exponential in the number of provers.