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Bounds on the size of small depth circuits for approximating majority
 In 36th Colloquium on Automata, Languages and Programming (ICALP
, 2009
"... Abstract. In this paper, we show that for every constant 0 < ǫ < 1/2 and for every constant d ≥ 2, the minimum size of a depth d Boolean circuit that ǫapproximates Majority function on n variables is exp(Θ(n 1/(2d−2))). The lower bound for every d ≥ 2 and the upper bound for d = 2 have been p ..."
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Abstract. In this paper, we show that for every constant 0 < ǫ < 1/2 and for every constant d ≥ 2, the minimum size of a depth d Boolean circuit that ǫapproximates Majority function on n variables is exp(Θ(n 1/(2d−2))). The lower bound for every d ≥ 2 and the upper bound for d = 2 have been
Lower Bounds For Uniform Constant Depth Circuits
, 1993
"... OF THE DISSERTATION Lower Bounds for Uniform Constant Depth Circuits by Vivek Kashinath Gore, Ph.D. Dissertation Director: Professor Eric Allender Boolean circuits were introduced in complexity theory to provide a model for parallel computation. A big advantage of studying Boolean circuits is that t ..."
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OF THE DISSERTATION Lower Bounds for Uniform Constant Depth Circuits by Vivek Kashinath Gore, Ph.D. Dissertation Director: Professor Eric Allender Boolean circuits were introduced in complexity theory to provide a model for parallel computation. A big advantage of studying Boolean circuits
On the size of depththree boolean circuits for computing multilinear functions
 Electronic Coll. on Computational Complexity (ECCC
"... We propose that multilinear functions of relatively low degree over GF(2) may be good candidates for obtaining exponential1 lower bounds on the size of constantdepth Boolean circuits (computing explicit functions). Specifically, we propose to move gradually from linear functions to multilinear on ..."
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Cited by 3 (0 self)
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to nested composition and yields depththree Boolean circuits via a ”guessandverify ” paradigm. The corresponding restricted models of circuits are called Dcanonical and NDcanonical, respectively. Our main results are (1) a generic upper bound on the size of depththree Dcanonical
Jacobian hits circuits: Hittingsets, lower bounds for depthD occurk formulas & depth3 transcendence degreek
"... circuits ..."
Bounds on the power of constantdepth quantum circuits. Preprint: quantph/0312209
 In Proc. 15th International Symposium on on Fundamentals of Computation Theory (FCT 2005), volume 3623 of Lecture Notes in Computer Science
, 2004
"... We show that if a language is recognized within certain error bounds by constantdepth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, for 0 < ɛ ≤ δ ≤ 1, we define BQNC 0 ɛ,δ to be the class of languages recognized by constant d ..."
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Cited by 19 (1 self)
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We show that if a language is recognized within certain error bounds by constantdepth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, for 0 < ɛ ≤ δ ≤ 1, we define BQNC 0 ɛ,δ to be the class of languages recognized by constant
Discrepancy and the power of bottom fanin in depththree circuits
 In Proc. of the 48th Symposium on Foundations of Computer Science (FOCS
, 2007
"... We develop a new technique of proving lower bounds for the randomized communication complexity of boolean functions in the multiparty ‘Number on the Forehead ’ model. Our method is based on the notion of voting polynomial degree of functions and extends the DegreeDiscrepancy Lemma in the recent wor ..."
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Cited by 26 (2 self)
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work of Sherstov [24]. Using this we prove that depth three circuits consisting of a MAJORITY gate at the output, gates computing arbitrary symmetric function at the second layer and arbitrary gates of bounded fanin at the base layer i.e. circuits of type MAJ ◦ SYMM ◦ ANY O(1) cannot simulate
Low depth quantum circuits for Ising models
 Annals of Physics
, 2014
"... A scheme for measuring complex temperature partition functions of Ising models is introduced. In the context of ordered qubit registers this scheme finds a natural translation in terms of global operations, and single particle measurements on the edge of the array. Two applications of this scheme ar ..."
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are presented. First, through appropriate Wick rotations, those amplitudes can be analytically continued to yield estimates for partition functions of Ising models. Bounds on the estimation error, valid with high confidence, are provided and shown to be compatible with previous results. Interestingly, the kind
Techniques for Analyzing the Computational Power of ConstantDepth Circuits and SpaceBounded Computation
, 2006
"... The subject of computational complexity theory is to analyze the difficulty of solving computational problems within different models of computation. Proving lower bounds is easier in less powerful models and proving upper bounds is easier in the more powerful models. This dissertation studies techn ..."
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of attention. We prove exponential lower bounds on the size of certain depththree circuits computing parity. Our approach is based on relating the lower bounds to correlation between parity and modular polynomials, and expressing the correlation with exponential sums. We show a new expression
Results 1  10
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110,887