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International Symposium on Mathematical Foundations of Computer Science

MFCS 2006: Mathematical Foundations of Computer Science 2006 pp 540–548Cite as

Reductions for Monotone Boolean Circuits

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

Abstract

The large class, say NLOG, of Boolean functions, including 0-1 Sort and 0-1 Merge, have an upper bound of O(nlogn) for their monotone circuit size, i.e., have circuits with O(nlogn) AND/OR gates of fan-in two. Suppose that we can use, besides such normal AND/OR gates, any number of more powerful “F-gates” which realize a monotone Boolean function F with r (≥2) inputs and r′ (≥1) outputs. Note that the cost of each AND/OR gate is one and we assume that the cost of each F-gate is r. Now we define: A Boolean function f in NLOG is said to be F-Easy if f can be constructed by a circuit with AND/OR/F gates whose total cost is o(nlogn). In this paper we show that 0-1 Merge is not F-Easy for an arbitrary monotone function F such that r′ ≤r/logr.

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Author information

Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Kazuo Iwama & Hiroki Morizumi

Authors
  1. Kazuo Iwama
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  2. Hiroki Morizumi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia

    Rastislav Královič

  2. Institute of Informatics, University of Warsaw, Poland

    Paweł Urzyczyn

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© 2006 Springer-Verlag Berlin Heidelberg

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Iwama, K., Morizumi, H. (2006). Reductions for Monotone Boolean Circuits. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_47

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  • DOI: https://doi.org/10.1007/11821069_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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