Limiting negations in bounded-depth circuits: an extension of Markov's theorem

Authors:
Shao Chin Sung;Keisuke Tanaka
Affiliations:
School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Tatsunokuchi, Ishikawa 923-1292, Japan;Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 1-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Venue:
Information Processing Letters
Year:
2004

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Abstract

A theorem of Markov shows the necessary and sufficient number of negations for computing an arbitrary collection of Boolean functions. In this paper, we consider a class of bounded-depth circuits, in which each gate computes an arbitrary monotone Boolean function or its negation. We show fight bounds on the number of negations for computing an arbitrary collection of Boolean functions when such a class of circuits is under consideration.