On the negation-limited circuit complexity of merging

Authors:
Kazuyuki Amano;Akira Maruoka;Jun Tarui
Affiliations:
Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Department of Communications and Systems, University of Electro-Communications, Chofu, Tokyo, Japan
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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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 x1 ≤...≤ xn and y1 ≤...≤ yn into a sequence z1 ≤...≤z2n. We prove that the size complexity of the (n, n) merging function with t = (log2 log2 n - a) NOT gates is Θ(2an).