Abstract

A negation-limited circuit is a combinational circuit that consists of AND, OR gates and a limited number of NOT gates. In this paper, we investigate the complexity of negation-limited circuits. The (n,n) merging function is a function that merges two presorted binary sequences \( x_1 \leqslant \cdots \leqslant x_n \) and \( y_1 \leqslant \cdots \leqslant y_n \) into a sequence \( z_1 \leqslant \cdots \leqslant z_{2n} \). We prove that the size complexity of the (n,n) merging function with \( t = \left( {\log _2 \log _2 n - a} \right) \) NOT gates is \( \Theta \left( {2^a n} \right) \).KeywordsBoolean FunctionCircuit ComplexityPartial AssignmentCombinational CircuitSmall CircuitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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