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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...
Some Topics in Parallel Computation and Branching Programs
, 1995
"... Some Topics in Parallel Computation and Branching Programs by Rakesh Kumar Sinha Chairperson of the Supervisory Committee: Professor Paul Beame Department of Computer Science and Engineering There are two parts of this thesis: the first part gives two constructions of branching programs; the second ..."
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Some Topics in Parallel Computation and Branching Programs by Rakesh Kumar Sinha Chairperson of the Supervisory Committee: Professor Paul Beame Department of Computer Science and Engineering There are two parts of this thesis: the first part gives two constructions of branching programs; the second part contains three results on models of parallel machines. The branching program model has turned out to be very useful for understanding the computational behavior of problems. In addition, several restrictions of branching programs, for example ordered binary decision diagrams, have proven to be successful data structures in several VLSI design and verification applications. We construct a branching program of o(n log 3 n) nodes for computing any threshold function on n variables and a branching program of o(n log 4 n) nodes for determining the sum of n variables modulo a fixed divisor. These are improvements over constructions of size 2(n 3=2 ) due to Lupanov [Lup65]. The second p...
Bit Extraction, HardCore Predicates, and the Bit Security Of RSA
, 1998
"... This thesis presents results on bit security and bit extraction. 1. A function ..."
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Cited by 1 (1 self)
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This thesis presents results on bit security and bit extraction. 1. A function
Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds
"... Abstract. Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, which gives a formula size lower bound by showing a feasible solution of the dual problem of its LPrelaxation. A ..."
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Abstract. Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, which gives a formula size lower bound by showing a feasible solution of the dual problem of its LPrelaxation. As extensions of the LP bound, we introduce novel general techniques proving formula size lower bounds, named a quasiadditive bound and the SheraliAdams bound. While the SheraliAdams bound is potentially strong enough to give a lower bound matching to the rectangle bound, we prove that the quasiadditive bound can surpass the rectangle bound. 1