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Annual Symposium on Theoretical Aspects of Computer Science

STACS 2006: STACS 2006 pp 660–671Cite as

Evaluating Monotone Circuits on Cylinders, Planes and Tori

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3884))

Abstract

We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC 3 in general, and in LogDCFL for the special case of upward stratified circuits. We characterize cylindricality, which is stronger than planarity but strictly generalizes upward planarity, and make the characterization partially constructive. We use this construction, and four key reduction lemmas, to obtain several improvements. We show that monotone circuits with embeddings that are stratified cylindrical, cylindrical, planar one-input-face and focused can be evaluated in LogDCFL, AC 1(LogDCFL), LogCFL and AC 1(LogDCFL) respectively. We note that the NC 3 algorithm for general MPCVP is in AC 1(LogCFL) = SAC 2. Finally, we show that monotone circuits with toroidal embeddings can, given such an embedding, be evaluated in NC.

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Author information

Authors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, 600 113, India

    Nutan Limaye, Meena Mahajan & M. N. Jayalal Sarma

Authors
  1. Nutan Limaye
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  2. Meena Mahajan
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  3. M. N. Jayalal Sarma
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Editor information

Editors and Affiliations

  1. LIF, CNRS & Univ. de Provence,, Marseille, France

    Bruno Durand

  2. RWTH Aachen University,, Lehrstuhl Informatik 7,, 52056,, Aachen,, Germany

    Wolfgang Thomas

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© 2006 Springer-Verlag Berlin Heidelberg

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Limaye, N., Mahajan, M., Jayalal Sarma, M.N. (2006). Evaluating Monotone Circuits on Cylinders, Planes and Tori. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_54

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  • DOI: https://doi.org/10.1007/11672142_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32301-3

  • Online ISBN: 978-3-540-32288-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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