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Monotone Circuits for Matching Require Linear Depth
"... We prove that monotone circuits computing the perfect matching function on nvertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits. ..."
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Cited by 77 (8 self)
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We prove that monotone circuits computing the perfect matching function on nvertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits.
Probabilistic Communication Complexity of Boolean Relations
 Proc. of the 30th FOCS
, 1989
"... In [KW] it was prooved that for every boolean function f there exist a communication complexity game R f such that the minimal circuitdepth of f exactly equals to the communication complexity of R f . If f is monotone then there also exists a game R m f with communication complexity exactly equal ..."
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Cited by 23 (7 self)
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In [KW] it was prooved that for every boolean function f there exist a communication complexity game R f such that the minimal circuitdepth of f exactly equals to the communication complexity of R f . If f is monotone then there also exists a game R m f with communication complexity exactly equals to the monotone depth of f . It was also prooved in [KW] that the communication complexity of R m st\Gammaconnectivity is\Omega\Gamma/34 2 n), or eqivalently that the monotone depth of the st connectivity function is\Omega\Gamma/38 2 n). In this paper we consider the games R f and R m f in a probabilistic model of communication complexity, and prove that the communication complexity of R m st\Gammaconnectivity is \Omega\Gamma/20 2 n) even in the probabilistic case. We also prove that in every NC1 circuit for st connectivity at least a constant fraction of all input variables must be negated. 1 Introduction In standard communication complexity, two players are trying to compute...