This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier to reject. Each team consists of two provers who jointly implement a no-signaling strategy. No-signaling strategies are a curious class of joint strategy that cannot in general be implemented without communication between the provers, yet cannot be used as a black box to establish communication between them. Attention is restricted in this paper to two-turn interactions in which the verifier asks questions of each of the four provers and decides whether to accept or reject based on their responses.

We prove that the complexity class of decision problems that admit two-turn interactive proofs with competing teams of no-signaling provers is a subset of PSPACE. This upper bound matches existing PSPACE lower bounds on the following two disparate and weaker classes of interactive proof:

1. Two-turn multi-prover interactive proofs with only one team of no-signaling provers.

2. Two-turn competing-prover interactive proofs with only one prover per team.

Our result implies that the complexity of these two models is unchanged by the addition of a second competing team of no-signaling provers in the first case and by the addition of a second no-signaling prover to each team in the second case. Moreover, our result unifies and subsumes prior PSPACE upper bounds on these classes.

Final version. Published in the Chicago Journal of Theoretical Computer Science, article 7, 2013.

This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier to reject. Each team consists of two provers who jointly implement a no-signaling strategy. No-signaling strategies are a curious class of joint strategy that cannot in general be implemented without communication between the provers, yet cannot be used as a black box to establish communication between them. Attention is restricted in this paper to two-turn interactions in which the verifier asks questions of each of the four provers and decides whether to accept or reject based on their responses.

We prove that the complexity class of decision problems that admit two-turn interactive proofs with competing teams of no-signaling provers is a subset of PSPACE. This upper bound matches existing PSPACE lower bounds on the following two disparate and weaker classes of interactive proof:

1. Two-turn multi-prover interactive proofs with only one team of no-signaling provers.

2. Two-turn competing-prover interactive proofs with only one prover per team.

Our result implies that the complexity of these two models is unchanged by the addition of a second competing team of no-signaling provers in the first case and by the addition of a second no-signaling prover to each team in the second case. Moreover, our result unifies and subsumes prior PSPACE upper bounds on these classes.

minor revisions, mostly to the introduction.

This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier to reject. Each team consists of two provers who jointly implement a no-signaling strategy. No-signaling strategies are a curious class of joint strategy that cannot in general be implemented without communication between the provers, yet cannot be used as a black box to establish communication between them. Attention is restricted in this paper to two-turn interactions in which the verifier asks questions of each of the four provers and decides whether to accept or reject based on their responses.

We prove that the complexity class of decision problems that admit two-turn interactive proofs with competing teams of no-signaling provers is a subset of PSPACE. This upper bound matches existing PSPACE lower bounds on the following two disparate and weaker classes of interactive proof:

1. Two-turn multi-prover interactive proofs with only one team of no-signaling provers.

2. Two-turn competing-prover interactive proofs with only one prover per team.

Our result implies that the complexity of these two models is unchanged by the addition of a second competing team of no-signaling provers in the first case and by the addition of a second no-signaling prover to each team in the second case. Moreover, our result unifies and subsumes prior PSPACE upper bounds on these classes.