Tradeoffs between Nondeterminism and Complexity for Communication Protocols and Branching Programs
One of the few major open problems concerning nondeterministic communication complexity is to prove an asymptotically exact tradeoff between complexity and the number of available advice bits. This problem is solved here for the case of one-way communication.
Multipartition protocols are introduced as a new type of communication protocols using a restricted form of non-obliviousness. In order to be able to study methods for proving lower bounds on multilective and/or non-oblivious computation, these protocols are allowed to either deterministically or nondeterministically choose between different partitions of the input. Here, the first results showing the potential increase of the computational power by non-obliviousness as well as boundaries on this power are derived.
The above results (and others) are applied to obtain several new exponential lower bounds for different types of oblivious branching programs, which also yields new insights into the power of nondeterminism and randomness for the considered models. The proofs rely on a general technique described here which allows to prove explicit lower bounds on the size of oblivious branching programs in an easy and transparent way.
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