We study non-deterministic communication protocols in which no input has too many witnesses. Define nk(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 nk(f). Our first result shows that nk(f) is below by Ω(√c(f)/k), where c(f) is the deterministic complexity. Our second results bounds nk(f) by log(rk(Mf))/k - 1, where rk(Mf) 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.
Bibliographical noteFunding Information:
In the two-party communication complexity model, two parties compute a function that depends on both of their (initially private) inputs. Roughly speaking, the deterministic communication complexity of a function f(x, y) is the minimum * Supported by NSF Grant CCR90-10533. t This work was done while the author was at the Royal Instituut of Technology, Stockholm. Supported in part by NSF Grant CCR89-11388, and AFOSR Grants 89-0512B and 90-0008.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics