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Evaluating Monotone Circuits on Cylinders, Planes and Tori

  • Nutan Limaye
  • Meena Mahajan
  • M. N. Jayalal Sarma
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Source Node Outgoing Edge Generalize Circuit Incoming Edge Span Subgraph 
These 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nutan Limaye
    • 1
  • Meena Mahajan
    • 1
  • M. N. Jayalal Sarma
    • 1
  1. 1.The Institute of Mathematical SciencesChennaiIndia

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