Abstract
We compare the complexities of Boolean functions for nondeterministic syntactic read- k-times branching and branching read- s k -times programs. It is shown that for each natural number k, k⩾2, there exists a sequence of Boolean functions such that the complexity of computation of each function of this sequence by nondeterministic syntactic branching read- k-times programs is exponentially larger (with respect to the number of variables of the Boolean function) than by nondeterministic branching read- (k ln k/ ln 2+C) -times programs, where C is a constant independent of k. Besides, it is shown that for each natural numbers N and k( N), where 4⩽k(N)<C 2 ln N / ln ln N and C 2< 2 is a constant independent of k and N, there exists a Boolean function in N variables such that the complexity of this function for nondeterministic syntactic read- k-times branching programs is exponentially larger (with respect to N) than for nondeterministic syntactic read- (k ln k/ ln 2+C) -times branching programs.
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