# On the hierarchy of nondeterministic branching *k*-programs

## Abstract

We compare the complexities of Boolean functions for nondeterministic read-*k*-times branching and read-*sk*-times branching programs. We show that for each natural number *k, k* ≥ 2, there exists a sequence of Boolean functions such that the complexity of computation of every function of this sequence by nondeterministic read-*k*-times branching programs is exponentially larger than by nondeterministic read-(*k* In *k*/ In 2 + *C*)-times branching programs (with respect to the number of variables of the Boolean function), where *C* is a constant independent of *k*. Besides it is shown that for each natural numbers *N* and *k*, \(4 \leqslant k \prec \sqrt {\ln N} /\ln \ln N\), there exists a Boolean function on *N* variables such that the complexity of this function for nondeterministic read-k-times branching programs is exponentially larger (on the number of variables of the Boolean function) than for nondeterministic read(*k* In *k*/ In 2 + *C*)-times branching programs.

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