Lower bounds for randomized read-k-times branching programs (extended abstract)

Abstract

Randomized branching programs are a probabilistic model of computation defined in analogy to the well-known probabilistic Turing machines. In this paper, we contribute to the complexity theory of randomized read-k-times branching programs. We first consider the case k = 1 and present a function which has nondeterministic read-once branching programs of polynomial size, but for which every randomized read-once branching program with two-sided error at most 27/128 is exponentially large. The same function also exhibits an exponential gap between the randomized read-once branching program sizes for different constant worst-case errors, which shows that there is no "probability amplification" technique for read-once branching programs which allows to decrease the error to an arbitrarily small constant by iterating probabilistic computations. Our second result is a lower bound for randomized read-k-times branching programs with two-sided error, where k > 1 is allowed. The bound is exponential for k < clog n, c an appropriate constant. Randomized read-k-times branching programs are thus one of the most general types of branching programs for which an exponential lower bound result could be established. © 1998 Springer-Verlag.