On the Power of Multi-Prover Interactive Protocols

Abstract We look at complexity issues of interactive proof systems with multiple provers separated from each other. This model, developed by Ben-Or et al. (1988) allows the verifier to play the provers off each other. We show this model equivalent to an alternative interactive proof system model using oracles as provers. We also show that every language accepted by these models lies in nondeterministic exponential time. We exhibit a relativized world where a co-NP language does not have multiple prover interactive proofs. Finally, we show a simple example that one cannot parallelize multiple prover protocols as easily as the single prover model.

[1]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[2]  Silvio Micali,et al.  Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems , 1991, JACM.

[3]  László Babai,et al.  Trading group theory for randomness , 1985, STOC '85.

[4]  Carsten Lund,et al.  Non-deterministic exponential time has two-prover interactive protocols , 2005, computational complexity.

[5]  Carsten Lund,et al.  Algebraic methods for interactive proof systems , 1992, JACM.

[6]  Lance Fortnow,et al.  Are There Interactive Protocols for CO-NP Languages? , 1988, Inf. Process. Lett..

[7]  Richard J. Lipton,et al.  PSPACE is provable by two provers in one round , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[8]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[9]  Joe Kilian,et al.  Uses of randomness in algorithms and protocols , 1990 .

[10]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[11]  Stathis Zachos,et al.  Does co-NP Have Short Interactive Proofs? , 1987, Inf. Process. Lett..

[12]  L. Fortnow.  Complexity-Theoretic Aspects of Interactive Proof Systems , 1989 .

[13]  Richard J. Lipton,et al.  On bounded round multiprover interactive proof systems , 1990, Proceedings Fifth Annual Structure in Complexity Theory Conference.

[14]  Adi Shamir,et al.  IP = PSPACE , 1992, JACM.

[15]  László Lovász,et al.  Two-prover one-round proof systems: their power and their problems (extended abstract) , 1992, STOC '92.

[16]  Carsten Lund,et al.  Algebraic methods for interactive proof systems , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[17]  László Babai,et al.  Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes , 1988, J. Comput. Syst. Sci..

[18]  Manuel Blum,et al.  Designing programs that check their work , 1989, STOC '89.

[19]  Oded Goldreich,et al.  On Completeness and Soundness in Interactive Proof Systems , 1989, Adv. Comput. Res..

[20]  László Lovász,et al.  Approximating clique is almost NP-complete , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[21]  Uriel Feige.  On the success probability of the two provers in one-round proof systems , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[22]  Avi Wigderson,et al.  Multi-prover interactive proofs: how to remove intractability assumptions , 2019, STOC '88.

[23]  L. Fortnow,et al.  On the power of multi-power interactive protocols , 1988, [1988] Proceedings. Structure in Complexity Theory Third Annual Conference.

[24]  Adi Shamir,et al.  Fully parallelized multi prover protocols for NEXP-time , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[25]  Silvio Micali,et al.  Byzantine agreement in constant expected time , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[26]  Lance Fortnow,et al.  The Complexity of Perfect Zero-Knowledge , 1987, Proceeding Structure in Complexity Theory.

[27]  Richard J. Lipton,et al.  On Games of Incomplete Information , 1992, Theor. Comput. Sci..

[28]  Sanjeev Arora,et al.  Probabilistic checking of proofs; a new characterization of NP , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[29]  Shafi Goldwasser,et al.  Private coins versus public coins in interactive proof systems , 1986, STOC '86.