Non-deterministic communication complexity with few witnesses

Nondeterministic communication protocols in which no input has too many witnesses are studied. Two different lower bounds are presented for n/sub k/(f), defined as the minimum complexity of a nondeterministic protocol for the function f in which each input has at most k witnesses. One result shows that n/sub k/(f) is bounded below by Omega ( square root c(f)/k) where c(f) is the deterministic complexity. A second result bounds n/sub k/(f) by log(rk(M/sub f/))/k-1, where rk(M/sub f/) is the rank of the representing matrix of f. It follows that the communication complexity analogue of the Turing-complexity class FewP is equal to the analogue of the class P.<<ETX>>

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