TY - JOUR
T1 - Non-deterministic communication complexity with few witnesses
AU - Karchmer, Mauricio
AU - Newman, Ilan
AU - Saks, Mike
AU - Wigderson, Avi
PY - 1994/10
Y1 - 1994/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0028518133&partnerID=8YFLogxK
U2 - 10.1016/S0022-0000(05)80049-2
DO - 10.1016/S0022-0000(05)80049-2
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AN - SCOPUS:0028518133
SN - 0022-0000
VL - 49
SP - 247
EP - 257
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
IS - 2
ER -