Comparing the sizes of nondeterministic branching read-k-times programs

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Abstract

We compare the complexities of Boolean functions for nondeterministic syntactic read-k-times branching and branching read-sk-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-(klnk/ln2+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)<C2lnN/lnlnN and C2<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-(klnk/ln2+C)-times branching programs.

Keywords

Branching program
Complexity
Boolean function

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Translated from Discrete Analysis and Operations Research, Novosibirsk, 6 (1) (1999) 65–85.

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Supported by the Russian Foundation for Fundamental Research (Grant 97-01-00848) and the Federal Target Program “Integration” (Project 473).