LTL Path Checking Is Efficiently Parallelizable
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Planarity, Determinants, Permanents, and (Unique) Matchings
ACM Transactions on Computation Theory (TOCT)
One-input-face MPCVP is hard for l, but in LogDCFL
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Evaluating monotone circuits on cylinders, planes and tori
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Planarity, determinants, permanents, and (unique) matchings
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
The complexity of the bootstraping percolation and other problems
Theoretical Computer Science
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Goldschlager first established that a special case of the monotone planar circuit problem can be solved by a Turing machine in $O(\log^2 n)$ space. Subsequently, Dymond and Cook refined the argument and proved that the same class can be evaluated in $O(\log^2 n)$ time with a polynomial number of processors. In this paper, we prove that the general monotone planar circuit value problem can be evaluated in $O(\log^4 n)$ time with a polynomial number of processors, settling an open problem posed by Goldschlager and Parberry.