Abstract
The 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 ⌈ log 2 ( 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.
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