Computational Complexity and Knowledge Complexity

TitleComputational Complexity and Knowledge Complexity
Publication TypeTechnical Report
Year of Publication1994
AuthorsGoldreich, O., Ostrovsky R., & Petrank E.
Other Numbers893

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^NP. Prior to this work, for languages with greater-than-zero knowledge complexity (and specifically, even for knowledge complexity 1) only trivial computational complexity bounds (i.e., only recognizability in PSPACE = IP) were known. In the course of our proof, we relate statistical knowledge-complexity with perfect knowledge-complexity; specifically, we show that, for the honest verifier, these hierarchies coincide, up to a logarithmic additive term (i.e., SKC(k(·)) ? PKC(k(·) + log(·))).

Bibliographic Notes

ICSI Technical Report TR-94-023

Abbreviated Authors

O. Goldreich, R. Ostrovsky, and E. Petrank

ICSI Publication Type

Technical Report