Probabilistic communication complexity
Journal of Computer and System Sciences
Lower bounds on communication complexity in distributed computer networks
Journal of the ACM (JACM)
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Lower bounds on communication complexity
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
On notions of information transfer in VLSI circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Rounds in communication complexity revisited
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Randomized versus nondeterministic communication complexity
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Nondeterministic communication with a limited number of advice bits
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The communication complexity of pointer chasing: applications of entropy and sampling
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Randomized Communication Protocols (A Survey)
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
On the Non-deterministic Communication Complexity of Regular Languages
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
ACM Transactions on Computation Theory (TOCT)
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We compare the communication complexity of discrete functions under different modes of computation, unifying and extending several known models. Protocols can be deterministic, nondeterministic or probabilistic and in the last case the error probability may vary. On the other hand communication can be 1-way, 2-way or as an intermediate stage consist of a fixed number k 1 of rounds.The following main results are obtained. A square gap between deterministic and nondeterministic communication complexity is shown for a specific function, which is the maximal possible. This improves the results of [MS 82] and [AUY 83]. For probabilistic 1- and 2-way protocols we prove linear lower bounds for functions that satisfy certain independence conditions, extending the results of [Y 79] and [Y 83]. Further, with more technical effort an exponential gap between deterministic k-round and probabilistic (k - 1)-round communication with fixed error probability is obtained. This generalizes the main result of [DGS 84]. On contrast for arbitrary error probabilities less than 1/2 there is no difference between the complexity of 1- and 2-way protocols, extending results of [PS 84]. Finally we consider communication with fixed message length and uniform probability distributions and give simulations of arbitrary protocols by such uniform ones with little overhead.