Non-deterministic communication complexity with few witnesses

Authors:
Mauricio Karchmer;Ilan Newman;Mike Saks;Avi Wigderson
Affiliations:
-;-;Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA and Department of CSE, University of California San Diego, La Jolla, California 92037, USA;-
Venue:
Journal of Computer and System Sciences
Year:
1994

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Abstract

We study non-deterministic communication protocols in which no input has too many witnesses. Define n"k(f) to be the minimum complexity of a non-deterministic protocol for the function f in which each input has at most k witnesses. We present two different lower bounds for n"k(f). Our first result shows that n"k(f) is below by @W(@/c(f)/k), where c(f) is the deterministic complexity. Our second results bounds n"k(f) by log(rk(M"f))/k - 1, where rk(M"f) is the rank of the representing matrix of f. As a consequence, it follows that the communication complexity analogue of the Turing-complexity class FewP is equal to the analogue of the class P.