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Limiting negations in non-deterministic circuits

By Hiroki Morizumi

Abstract

AbstractThe minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f. In 1958, Markov determined the inversion complexity of every Boolean function and, in particular, proved that ⌈log2(n+1)⌉ NOT gates are sufficient to compute any Boolean function on n variables. In this paper, we consider circuits computing non-deterministically and determine the inversion complexity of every Boolean function. In particular, we prove that one NOT gate is sufficient to compute any Boolean function in non-deterministic circuits if we can use an arbitrary number of guess inputs

Publisher: Elsevier B.V.
Year: 2009
DOI identifier: 10.1016/j.tcs.2009.05.018
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