Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
E. Petrank , Dept. of Comput. Sci., Toronto Univ., Ont., Canada
G. Tardos , Dept. of Comput. Sci., Toronto Univ., Ont., Canada
The authors show that if a language has an interactive proof of logarithmic statistical knowledge-complexity, then it belongs to the class A M ∩ co− A M. Thus, if the polynomial time hierarchy does not collapse, then N P−complete languages do not have logarithmic knowledge complexity. Prior to this work, there was no indication that would contradict N P languages being proven with even one bit of knowledge. Next, they consider the relation between the error probability and the knowledge complexity of an interactive proof. They show that if the error probability ε(n) is less than 2 -3k(n) (where k(n) is the knowledge complexity) then the language proven has to be in the third level of the polynomial time hierarchy. In order to prove their main result, they develop an A M protocol for checking that a samplable distribution has a given entropy. They believe that this protocol is of independent interest.
computational complexity; language; interactive proof; logarithmic statistical knowledge complexity; polynomial time hierarchy; NP-complete languages; error probability; samplable distribution entropy
G. Tardos and E. Petrank, "On the knowledge complexity of N P," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 494.