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Quantum Circuit Complexity
, 1993
"... We study a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomialsize quantum circuit. This result also enables us to construct a universal quantum compu ..."
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Cited by 319 (1 self)
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We study a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomialsize quantum circuit. This result also enables us to construct a universal quantum
Circuit Complexity

"... Combinational circuits or shortly circuits are a model of the lowest level of computer hardware which is of interest from the point of view of computer science. Circuit complexity has a longer history than complexity theory. Complexity measures like circuit size and depth model sequential time, ..."
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Combinational circuits or shortly circuits are a model of the lowest level of computer hardware which is of interest from the point of view of computer science. Circuit complexity has a longer history than complexity theory. Complexity measures like circuit size and depth model sequential time
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
"... 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 to calcu ..."
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Cited by 328 (1 self)
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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
THE BROKENCIRCUIT COMPLEX
, 1977
"... The brokencircuit complex introduced by H. Wilf (Which polynomials are chromatic!, Proc. Colloq. Combinational Theory (Rome, 1973)) of a matroid G is shown to be a cone over a related complex, the reduced brokencircuit complex Q'(G). The topological structure of Q'(G) is studied, its E ..."
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Cited by 33 (0 self)
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The brokencircuit complex introduced by H. Wilf (Which polynomials are chromatic!, Proc. Colloq. Combinational Theory (Rome, 1973)) of a matroid G is shown to be a cone over a related complex, the reduced brokencircuit complex Q'(G). The topological structure of Q'(G) is studied, its
On the brokencircuit complex of graphs
"... It is wellknown that the StanleyReisner ring of a matroid complex is level; this is an algebraic property between the CohenMacaulay and Gorenstein properties. A similar result for brokencircuit complexes is no longer true, even for graphs. We show that the StanleyReisner ring of the brokencirc ..."
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It is wellknown that the StanleyReisner ring of a matroid complex is level; this is an algebraic property between the CohenMacaulay and Gorenstein properties. A similar result for brokencircuit complexes is no longer true, even for graphs. We show that the StanleyReisner ring of the brokencircuit
The monotone circuit complexity of Boolean functions
 COMBINATORICA
, 1987
"... Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that lect cliques in graphs. In particular, Razborov showed that detecting cliques of size s in a graph dh m vertices requires monotone circuits of size.Q(m'/(log m) ~') for fixed s, and size rn ao°~') for ..."
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Cited by 144 (2 self)
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Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that lect cliques in graphs. In particular, Razborov showed that detecting cliques of size s in a graph dh m vertices requires monotone circuits of size.Q(m'/(log m) ~') for fixed s, and size rn ao
Circuit Complexity and Computational Complexity
, 1992
"... Introduction to circuit complexity. Theorems of Shannon and Lupanov giving upper and lower bounds of circuit complexity of almost all Boolean functions. January 1421. Matt Clegg's notes on Spira's theorem relating depth and formula size Krapchenko's lower bound on formula size over ..."
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Introduction to circuit complexity. Theorems of Shannon and Lupanov giving upper and lower bounds of circuit complexity of almost all Boolean functions. January 1421. Matt Clegg's notes on Spira's theorem relating depth and formula size Krapchenko's lower bound on formula size over
Circuit complexity of regular languages
, 2007
"... We survey our current knowledge of circuit complexity of regular languages and we prove that regular languages that are in AC 0 and ACC 0 are all computable by almost linear size circuits, extending the result of Chandra et. al [5]. As a consequence we obtain that in order to separate ACC 0 from NC ..."
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We survey our current knowledge of circuit complexity of regular languages and we prove that regular languages that are in AC 0 and ACC 0 are all computable by almost linear size circuits, extending the result of Chandra et. al [5]. As a consequence we obtain that in order to separate ACC 0 from NC
VC Dimension in Circuit Complexity
 In Proceedings of the 11th Annual IEEE Conference on Computational Complexity CCC'96
, 1995
"... The main result of this paper is a \Omega\Gamma n 1=4 ) lower bound on the size of a sigmoidal circuit computing a specific AC 0 2 function. This is the first lower bound for the computation model of sigmoidal circuits with unbounded weights. We also give upper and lower bounds for the same funct ..."
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Cited by 6 (1 self)
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function in a few other computation models: circuits of AND/OR gates, threshold circuits, and circuits of piecewiserational gates. 1 Introduction One of the main trends in circuit complexity has been to establish lower bounds for circuits made of increasingly powerful gates. Threshold circuits have been
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 2821 (11 self)
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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
Results 1  10
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333,372