Abstract
A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the one-input-face monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that evaluating monotone upward stratified circuits, a restricted version of the one-input-face MPCVP, is in LogDCFL. In this paper, we prove that the unrestricted one-input-face MPCVP is also in LogDCFL. We also show this problem to be L-hard under quantifier free projections.
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Chakraborty, T., Datta, S. (2006). One-Input-Face MPCVP Is Hard for L, But in LogDCFL. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_8
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DOI: https://doi.org/10.1007/11944836_8
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