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ON THRESHOLD CIRCUITS AND POLYNOMIAL COMPUTATION
"... A Threshold Circuit consists of an acyclic digraph of unbounded fanin, where each node computes a threshold function or its negation. This paper investigates the computational power of Threshold Circuits. A surprising relationship is uncovered between Threshold Circuits and another class of unbound ..."
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Cited by 60 (1 self)
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A Threshold Circuit consists of an acyclic digraph of unbounded fanin, where each node computes a threshold function or its negation. This paper investigates the computational power of Threshold Circuits. A surprising relationship is uncovered between Threshold Circuits and another class
On the Power of SmallDepth Threshold Circuits
, 1990
"... We investigate the power of threshold circuits of small depth. In particular we give functions which require exponential size unweigted threshold circuits of depth 3 when we restrict the bottom fanin. We also prove that there are mone tone functions fk which can be computed in depth k and linear s ..."
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Cited by 124 (2 self)
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We investigate the power of threshold circuits of small depth. In particular we give functions which require exponential size unweigted threshold circuits of depth 3 when we restrict the bottom fanin. We also prove that there are mone tone functions fk which can be computed in depth k and linear
Exact threshold circuits
 In IEEE Conf. on Computational Complexity (CCC
, 2010
"... Abstract—We initiate a systematic study of constant depth Boolean circuits built using exact threshold gates. We consider both unweighted and weighted exact threshold gates and introduce corresponding circuit classes. We next show that this gives a hierarchy of classes that seamlessly interleave wit ..."
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Cited by 3 (0 self)
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Abstract—We initiate a systematic study of constant depth Boolean circuits built using exact threshold gates. We consider both unweighted and weighted exact threshold gates and introduce corresponding circuit classes. We next show that this gives a hierarchy of classes that seamlessly interleave
Root finding with threshold circuits
, 2011
"... We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials—given by a list of coefficients in binary—can be computed to a given accuracy by a uniform TC 0 algorithm (a uniform family of constantdepth polynomialsize threshold circuits). The bas ..."
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Cited by 2 (0 self)
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We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials—given by a list of coefficients in binary—can be computed to a given accuracy by a uniform TC 0 algorithm (a uniform family of constantdepth polynomialsize threshold circuits
On Proofs About Threshold Circuits and
"... We define theories of Bounded Arithmetic characterizing classes of functions computable by constantdepth threshold circuits of polynomial and quasipolynomial size. Then we define certain secondorder theories and show that they characterize the functions in the Counting Hierarchy. Finally we sho ..."
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We define theories of Bounded Arithmetic characterizing classes of functions computable by constantdepth threshold circuits of polynomial and quasipolynomial size. Then we define certain secondorder theories and show that they characterize the functions in the Counting Hierarchy. Finally we
Simulating Threshold Circuits by Majority Circuits
 SIAM JOURNAL ON COMPUTING
, 1994
"... We prove that a single threshold gate with arbitrary weights can be simulated by an explicit polynomialsize depth 2 majority circuit. In general we show that a depth d threshold circuit can be simulated uniformly by a majority circuit of depth d + 1. Goldmann, Hastad, and Razborov showed in [10 ..."
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Cited by 36 (0 self)
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We prove that a single threshold gate with arbitrary weights can be simulated by an explicit polynomialsize depth 2 majority circuit. In general we show that a depth d threshold circuit can be simulated uniformly by a majority circuit of depth d + 1. Goldmann, Hastad, and Razborov showed
Threshold Circuits of Small MajorityDepth
 Information and Computation
, 1995
"... Constantdepth polynomialsize threshold circuits are usually classified according to their total depth. For example, the best known threshold circuits for iterated multiplication and division have depth four and three, respectively. In this paper, the complexity of threshold circuits is investigate ..."
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Cited by 14 (3 self)
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Constantdepth polynomialsize threshold circuits are usually classified according to their total depth. For example, the best known threshold circuits for iterated multiplication and division have depth four and three, respectively. In this paper, the complexity of threshold circuits
On Small Depth Threshold Circuits
 PROCEEDINGS OF THE 3RD SWAT SCANDINAVIAN WORKSHOP ON ALGORITHM THEORY, HELSINKI, FINLAND (LNCS 621
, 1992
"... In this talk we will consider various classes defined by small depth polynomial size circuits which contain threshold gates and parity gates. We will describe various inclusions between many classes defined in this way and also classes whose definitions rely upon spectral properties of Boolean fu ..."
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Cited by 26 (2 self)
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In this talk we will consider various classes defined by small depth polynomial size circuits which contain threshold gates and parity gates. We will describe various inclusions between many classes defined in this way and also classes whose definitions rely upon spectral properties of Boolean
Optimization of DualThreshold Circuits
, 2005
"... In this paper, we consider an optimization problem on directed acyclic graphs which is motivated by a standard task in low power VLSI design. With each vertex v of a directed acyclic graph, we associate two delay values d0(v) ≤ d1(v) and two leakage values c0(v) ≥ c1(v). The objective is to choose ..."
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heuristic approaches to the problem. Further, we test our algorithms on ISCAS85 benchmark circuits.
Results 1  10
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165,949