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FixedPolynomial Size Circuit Bounds
"... Abstract—In 1982, Kannan showed that Σ P 2 does not have n ksized circuits for any k. Do smaller classes also admit such circuit lower bounds? Despite several improvements of Kannan’s result, we still cannot prove that P NP does not have linear size circuits. Work of Aaronson and Wigderson provides ..."
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Cited by 4 (0 self)
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provides strong evidence – the “algebrization ” barrier – that current techniques have inherent limitations in this respect. We explore questions about fixedpolynomial size circuit lower bounds around and beyond the algebrization barrier. We find several connections, including The following are equivalent
Almost Optimal Lower Bounds for Small Depth Circuits
, 1986
"... 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 277 (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
Boundedwidth polynomialsize branching programs recognize exactly those languages
 in NC’, in “Proceedings, 18th ACM STOC
, 1986
"... We show that any language recognized by an NC ’ circuit (fanin 2, depth O(log n)) can be recognized by a width5 polynomialsize branching program. As any boundedwidth polynomialsize branching program can be simulated by an NC ’ circuit, we have that the class of languages recognized by such prog ..."
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Cited by 270 (14 self)
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We show that any language recognized by an NC ’ circuit (fanin 2, depth O(log n)) can be recognized by a width5 polynomialsize branching program. As any boundedwidth polynomialsize branching program can be simulated by an NC ’ circuit, we have that the class of languages recognized
Parallel Prefix Computation
 JOURNAL OF THE ACM
, 1980
"... The prefix problem is to compute all the products x t o x2.... o xk for i ~ k. ~ n, where o is an associative operation A recursive construction IS used to obtain a product circuit for solving the prefix problem which has depth exactly [log:n] and size bounded by 4n An application yields fast, smal ..."
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Cited by 337 (1 self)
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The prefix problem is to compute all the products x t o x2.... o xk for i ~ k. ~ n, where o is an associative operation A recursive construction IS used to obtain a product circuit for solving the prefix problem which has depth exactly [log:n] and size bounded by 4n An application yields fast
Lower Bounds for the Size of Circuits of Bounded Depth in Basis
, 1986
"... this paper, we consider circuits of bounded depth in the basis f; \Phig. ..."
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Cited by 86 (0 self)
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this paper, we consider circuits of bounded depth in the basis f; \Phig.
Faulttolerant quantum computation
 In Proc. 37th FOCS
, 1996
"... It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information i ..."
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Cited by 264 (5 self)
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as originally believed. For any quantum computation with t gates, we show how to build a polynomial size quantum circuit that tolerates O(1 / log c t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O(1 /t). We do this by showing that operations can be performed
Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds (Extended Abstract)
, 2003
"... Since Polynomial Identity Testing is a coRP problem, we obtain the following corollary: If RP = P (or, even, coRP ` "ffl?0NTIME(2nffl), infinitely often), then NEXP is not computable by polynomialsize arithmetic circuits. Thus, establishing that RP = coRP or BPP = P would require proving s ..."
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Cited by 175 (5 self)
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Since Polynomial Identity Testing is a coRP problem, we obtain the following corollary: If RP = P (or, even, coRP ` "ffl?0NTIME(2nffl), infinitely often), then NEXP is not computable by polynomialsize arithmetic circuits. Thus, establishing that RP = coRP or BPP = P would require proving
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
On MediumUniformity and Circuit Lower Bounds
"... Abstract—We explore relationships between circuit complexity, the complexity of generating circuits, and algorithms for analyzing circuits. Our results can be divided into two parts: 1. Lower Bounds Against MediumUniform Circuits. Informally, a circuit class is “medium uniform ” if it can be genera ..."
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Cited by 3 (1 self)
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(n k). That is, for all k there is a language Lk ∈ P that does not have O(n k)size circuits constructible in polynomial time. This improves Kannan’s lower bound from 1982 that NP is not in Puniform SIZE(n k) for any fixed k.
Test Set Compaction Algorithms for Combinational Circuits
, 2000
"... This paper presents a new algorithm, Essential Fault Reduction (EFR), for generating compact test sets for combinational circuits under the single stuckat fault model, and a new heuristic for estimating the minimum single stuckat fault test set size. These algorithms together with the dynamic co ..."
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Cited by 156 (5 self)
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This paper presents a new algorithm, Essential Fault Reduction (EFR), for generating compact test sets for combinational circuits under the single stuckat fault model, and a new heuristic for estimating the minimum single stuckat fault test set size. These algorithms together with the dynamic
Results 1  10
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