Branching programs are a well-established computation model
for Boolean functions, especially read-once branching programs
have been studied intensively. Exponential lower bounds for
deterministic and nondeterministic read-once branching programs
are known for a long time. On the other hand, the problem of
proving superpolynomial lower bounds ... more >>>

The ``log rank'' conjecture consists in the question how exact
the deterministic communication complexity of a problem can be
determinied in terms of algebraic invarants of the communication
matrix of this problem. In the following, we answer this question
in the context of modular communication complexity. ... more >>>

We investigate the probabilistic communication complexity
(more exactly, the majority communication complexity,)
of the graph accessibility problem GAP and
its counting versions MOD_k-GAP, k > 1.
Due to arguments concerning matrix variation ranks
and certain projection reductions, we prove
that, for any partition of the input variables,
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We prove that the modular communication complexity of the
undirected graph connectivity problem UCONN equals Theta(n),
in contrast to the well-known Theta(n*log n) bound in the
deterministic case, and to the Omega(n*loglog n) lower bound
in the nondeterministic case, recently proved by ... more >>>