Interactive proofs with competing teams of no-signaling provers
Chic. J. Theor. Comput. Sci.(2010)
摘要
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.
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