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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 84 (9 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
 in \Proc. of 30th Annual IEEE Symp. on Foundations of Computer Science
, 1989
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Some Topics in Parallel Computation and Branching Programs
, 1995
"... 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 ..."
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Cited by 2 (0 self)
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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
Discovery of Concurrent Data Models from Experimental Tables: A Rough Set Approach
"... The main objective of machine discovery is the determination of relations between data and of data models. In the paper we describe a method for discovery of data models represented by concurrent systems from experimental tables. The basic step consists in a determination of roles which yield a dec ..."
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The main objective of machine discovery is the determination of relations between data and of data models. In the paper we describe a method for discovery of data models represented by concurrent systems from experimental tables. The basic step consists in a determination of roles which yield a decomposition of experimental data tables; the components are then used to define fragments of the global system corresponding to a table. The method has been applied for automatic data models discovery from experimental tables with Petri nets as models for concurrency. Key words: data mining, system decomposition, rough sets, concurrent models
vices. Monotone Circuits for Matching Require Linear Depth
, 2003
"... We prove that monotone circuits computing the perfect matching function on nvertex graphs require Ω(n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits. ..."
Abstract
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We prove that monotone circuits computing the perfect matching function on nvertex graphs require Ω(n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits.