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585,595
Definability by constantdepth polynomialsize circuits
 Information and Control
, 1986
"... A function of boolean arguments is symmetric if its value depends solely on the number of l's among its arguments. In the first part of this paper we partially characterize those symmetric functions that can be computed by constantdepth polynomialsize sequences of boolean circuits, and discus ..."
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Cited by 18 (0 self)
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to circuits recognizing firstorder structures. By imposing fairly natural restrictions we develop a circuit model with precisely the power of firstorder logic: a class of structures is firstorder definable if and only if it can be recognized by a constantdepth polynomialtime sequence of such circuits
Constantdepth circuits for arithmetic in finite fields of characteristic two
 IN PROCEEDINGS OF THE 23RD INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS), LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... We study the complexity of arithmetic in finite fields of characteristic two, F2n. We concentrate on the following two problems: • Iterated Multiplication: Given α1, α2,...,αt ∈ F2 n, compute α1 · α2 · · ·αt ∈ F2 n. • Exponentiation: Given α ∈ F2 n and a tbit integer k, compute αk ∈ F2 n. ..."
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Cited by 16 (9 self)
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We study the complexity of arithmetic in finite fields of characteristic two, F2n. We concentrate on the following two problems: • Iterated Multiplication: Given α1, α2,...,αt ∈ F2 n, compute α1 · α2 · · ·αt ∈ F2 n. • Exponentiation: Given α ∈ F2 n and a tbit integer k, compute αk ∈ F2 n.
A logic for constantdepth circuits
 Information and Control
, 1984
"... Consider a family of boolean circuits C~, C2,..., C,,..., constructed by some uniform, effective procedure operating on input n. Such a procedure provides a concise representation of a family of parallel algorithms for computing boolean values. A formula of firstorder logic may also be viewed as a ..."
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Cited by 18 (3 self)
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, constantdepth, unboundedfanin circuits constructed by Turing machines of bounded computational complexity. © 1984 Academic Press, Inc. Several papers (Chandra et al., 1983a; Chandra et al., 1982; Chandra et al., 1983b; Furst et al., 1981; Sipser, 1983) have recently dealt with the
Lower Bounds to the Size of ConstantDepth Propositional Proofs
, 1994
"... 1 LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives : and V ; W (both of unbounded arity). Then for every d 0 and n 2, there is a set T d n of depth d sequents of total size O(n 3+d ) which are refutable in LK by depth d + 1 proof of size exp ..."
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Cited by 56 (7 self)
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exp(O(log 2 n)) but such that every depth d refutation must have the size at least exp(n\Omega\Gamma21 ). The sets T d n express a weaker form of the pigeonhole principle. It is a fundamental problem of mathematical logic and complexity theory whether there exists a proof system for propositional
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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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
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs
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
On the ConstantDepth Complexity of kClique
"... We prove a lower bound of ω(n k/4) on the size of constantdepth circuits solving the kclique problem on nvertex graphs (for every constant k). This improves a lower bound of ω(n k/89d2) due to Beame where d is the circuit depth. Our lower bound has the advantage that it does not depend on the cons ..."
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Cited by 13 (3 self)
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We prove a lower bound of ω(n k/4) on the size of constantdepth circuits solving the kclique problem on nvertex graphs (for every constant k). This improves a lower bound of ω(n k/89d2) due to Beame where d is the circuit depth. Our lower bound has the advantage that it does not depend
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
Results 1  10
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585,595