On Completeness and Soundness in Interactive Proof Systems

{ An interactive proof system with Perfect Completeness (resp. Perfect Soundness) for a language L is an interactive proof (for L) in which for every x 2 L (resp. x 6 2 L) the veriier always accepts (resp. always rejects). We show that any language having an interactive proof system has one (of the Arthur-Merlin type) with perfect completeness. On the other hand, only languages in NP have interactive proofs with perfect soundness.

[1]  Leonard M. Adleman,et al.  Two theorems on random polynomial time , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[2]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[3]  Michael Sipser,et al.  A complexity theoretic approach to randomness , 1983, STOC.

[4]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

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

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

[7]  Stathis Zachos,et al.  A Decisive Characterization of BPP , 1986, Inf. Control..

[8]  Janos Simon,et al.  BPP and the polynomial time hierarchy in communication complexity , 1986 .

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

[10]  Yair Oren,et al.  On the cunning power of cheating verifiers: Some observations about zero knowledge proofs , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[11]  Stathis Zachos,et al.  Probabalistic Quantifiers vs. Distrustful Adversaries , 1987, FSTTCS.

[12]  Oded Goldreich,et al.  Interactive proof systems: Provers that never fail and random selection , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[13]  Uwe Schöning Probabilistic Complexity Classes and Lowness , 1989, J. Comput. Syst. Sci..

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