Abstract
A monotone boolean circuit is said to be multilinear if for any AND gate in the circuit, the minimal representation of the two input functions to the gate do not have any variable in common. We show that multilinear boolean circuits for bipartite perfect matching require exponential size. In fact we prove a stronger result by characterizing the structure of the smallest multilinear boolean circuits for the problem. We also show that the upper bound on the minimum depth of monotone circuits for perfect matching in general graphs is O(n).
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Ponnuswami, A.K., Venkateswaran, H. (2004). Monotone Multilinear Boolean Circuits for Bipartite Perfect Matching Require Exponential Size. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_38
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DOI: https://doi.org/10.1007/978-3-540-30538-5_38
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