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Algebraic methods in the theory of lower bounds for boolean circuit complexity
 In Proceedings of the 19th Annual ACM Symposium on Theory of Computing, STOC ’87
, 1987
"... kbstr act We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fanin circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MOD, where p is a prime require Ezp(O(n’)) gates ..."
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Cited by 331 (1 self)
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kbstr act We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fanin circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MOD, where p is a prime require Ezp
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
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Cited by 3499 (47 self)
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In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Almost Optimal Lower Bounds for Small Depth Circuits
 RANDOMNESS AND COMPUTATION
, 1989
"... We give improved lower bounds for the size of small depth circuits computing several functions. In particular we prove almost optimal lower bounds for the size of parity circuits. Further we show that there are functions computable in polynomial size and depth k but requires exponential size when ..."
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Cited by 280 (8 self)
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We give improved lower bounds for the size of small depth circuits computing several functions. In particular we prove almost optimal lower bounds for the size of parity circuits. Further we show that there are functions computable in polynomial size and depth k but requires exponential size
SIS: A System for Sequential Circuit Synthesis
, 1992
"... SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential inputoutput b ..."
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Cited by 514 (41 self)
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SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential input
An Exponential Lower Bound for Depth 3 Arithmetic Circuits
, 1998
"... We prove the first exponential lower bound on the size of any depth 3 arithmetic circuit with unbounded fanin computing an explicit function (the determinant) over an arbitrary finite field. This answers an open problem of [N91] and [NW95] for the case of finite fields. We intepret here arithmetic c ..."
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Cited by 55 (1 self)
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We prove the first exponential lower bound on the size of any depth 3 arithmetic circuit with unbounded fanin computing an explicit function (the determinant) over an arbitrary finite field. This answers an open problem of [N91] and [NW95] for the case of finite fields. We intepret here arithmetic
Realtime human pose recognition in parts from single depth images
 In In CVPR, 2011. 3
"... We propose a new method to quickly and accurately predict 3D positions of body joints from a single depth image, using no temporal information. We take an object recognition approach, designing an intermediate body parts representation that maps the difficult pose estimation problem into a simpler p ..."
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Cited by 550 (19 self)
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We propose a new method to quickly and accurately predict 3D positions of body joints from a single depth image, using no temporal information. We take an object recognition approach, designing an intermediate body parts representation that maps the difficult pose estimation problem into a simpler
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
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Cited by 2837 (11 self)
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;enyi's nonmonotone result [Imm88, Sze87] that NL = coNL; this is a simple extension of the monotone circuit depth lower bound of Karchmer and Wigderson [KW90] for stconnectivity. We also consider mBWBP (monotone bounded width branching programs) and study the question of whether mBWBP is properly contained
Symbolic Model Checking without BDDs
, 1999
"... Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis ..."
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Cited by 910 (74 self)
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Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis
Results 1  10
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