Appeared I N Siam Journal on Computing Computational Complexity and Knowledge Complexity Appeared I N Siam Journal on Computing

We study the computational complexity of languages which have interactive proofs of logarithmic knowledge-complexity. We show that all such languages can be recognized in BPP . Prior to this work, for languages with greater-than-zero knowledge-complexity only trivial computational complexity bounds were known. In the course of our proof, we relate statistical knowledgecomplexity with perfect knowledge-complexity; speci cally, we show that, for the honest veri er, these hierarchies coincide, up to a logarithmic additive term. An extended abstract of this paper appeared in the 26th ACM Symposium on Theory of Computing (STOC 94), held in Montreal, Quebec, Canada, May 23-25, 1994. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel. E-mail: [email protected]. Supported by grant no. 92-00226 from the United States | Israel Binational Science Foundation, Jerusalem, Israel. Bell Communications Research, 445 South Street, Morristown, New Jersey 07960-6438. E-mail: [email protected]. Part of this work was done at University of California at Berkeley and International Computer Science Institute at Berkeley and supported by an NSF postdoctoral fellowship and ICSI. Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4. E-mail: [email protected]