# Lower bounds for randomized read-*k*-times branching programs

## 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 read-*k*-times = 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.

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