Communication Complexity and Quasi Randomness

Complexity and Quasi - randomness 1

Many problems arising in interactive and distributive computation share the general framework that a number of processors wish to collaboratively evaluate a Boolean function while each processor has only partial information. The question of interest is to determine the minimum amount of information transfer required under the assumption that each processor has unlimited computational power and ...

Public vs. Private Randomness in Simultaneous Multi-party Communication Complexity

In simultaneous number-in-hand multi-party communication protocols, we have k players, who each receive a private input, and wish to compute a joint function of their inputs. The players simultaneously each send a single message to a referee, who then outputs the value of the function. The cost of the protocol is the total number of bits sent to the referee. For two players, it is known that gi...

Lower bound for communication complexity with no public randomness

We give a self contained proof of a logarithmic lower bound on the communication complexity of any non redundant function, given that there is no access to shared randomness. This bound was first stated in Yao’s seminal paper [STOC 1979], but no full proof appears in the literature. Our proof uses the method of Babai and Kimmel [Computational Complexity 1997], introduced there in the context of...

Algorithmic Randomness and Complexity

Complexity and Randomness

2 Random finite strings 7 2.1 Plain Kolmogorov complexity . . . . . . . . . . . . . . . . . . 7 2.2 Prefix-free complexity . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Kraft inequality, Shannon-Fano code . . . . . . . . . . . . . . 9 2.4 The universal semimeasure m . . . . . . . . . . . . . . . . . . 10 2.5 A priori probability . . . . . . . . . . . . . . . . . . . . . . . . 11 2.6 Coding,...