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Measuring communication complexity using instance complexity with oracles
We establish a connection between non-deterministic communication complexity
and instance complexity, a measure of information based on algorithmic entropy.
Let , and be respectively the
input known by Alice, the input known by Bob, and the set of all values of
such that ; a string is a witness of the non-deterministic
communication protocol iff it is a program that "corresponds exactly" to
the instance complexity \ic^{f,t}(\overline{y}:Y_1(\overline{x}))