A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2004; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Uniform constant-depth threshold circuits for division and iterated multiplication

2002
*
Journal of computer and system sciences (Print)
*

1 2 HESSE, ALLENDER

doi:10.1016/s0022-0000(02)00025-9
fatcat:vwqdpnv7njghzi2326rxqprtca
*AND*BARRINGTON It has been known since the mid-1980's [15, 46, 47] that integer*division*can be performed by poly-time*uniform**constant*-*depth**circuits*of Majority gates; equivalently ... Recently this was improved to L-*uniform*TC 0 [19], but it remained unknown whether*division*can be performed by DLOGTIME-*uniform*TC 0*circuits*. ... We also thank Dieter van Melkebeek, Samir Datta, Michal Koucký, Rüdiger Reischuk,*and*Sambuddha Roy*for*helpful discussions. ...##
###
On Threshold Circuits and Polynomial Computation

1992
*
SIAM journal on computing (Print)
*

A surprising relationship is uncovered between

doi:10.1137/0221053
fatcat:4sagnkbzy5fq5csptjebulmvu4
*Threshold**Circuits**and*another class of unbounded fanin*circuits*which are denoted Finite Field Z P (n) ... This paper investigates the computational power of*Threshold**Circuits*. ... Pippenger has given a*constant**depth**threshold**circuit**for**multiplication*,*and*the method used is the straight-forward reduction to*iterated*sum (i.e., the \gradeschool method" of*multiplication*) 17]. ...##
###
Division Is In Uniform TC0
[chapter]

2001
*
Lecture Notes in Computer Science
*

Integer

doi:10.1007/3-540-48224-5_9
fatcat:vu6dhiadb5drjduq47va4sfobq
*division*has been known since 1986 [4, 13, 12] to be in slightly non-*uniform*TC 0 , i.e., computable by polynomial-size,*constant**depth**threshold**circuits*. ... This has been perhaps the outstanding natural problem known to be in a standard*circuit*complexity class, but not known to be in its*uniform*version. We show that indeed*division*is in*uniform*TC 0 . ... In this paper, we construct*uniform**constant**depth**circuits**for**division**and**iterated**multiplication*. ...##
###
Threshold Circuits for Iterated Matrix Product and Powering

2000
*
RAIRO - Theoretical Informatics and Applications
*

As computational model, we use

doi:10.1051/ita:2000105
fatcat:qf4stv4pnraxhgq7kdbrazfv6q
*threshold**circuits*[12] . We are interested in solving problems by using*threshold**circuits*of*constant**depth*. ... We recall that TC^ is the class of probiems solvable by families of (unbounded fan-in)*threshold**circuits*of polynomial weights*and*size,*and**constant**depth*d. ...##
###
Root finding with threshold circuits

2012
*
Theoretical Computer Science
*

*uniform*TC^0 algorithm (a

*uniform*family of

*constant*-

*depth*polynomial-size

*threshold*

*circuits*). ... We show that

*for*any

*constant*d, complex roots of degree d univariate rational (or Gaussian rational) polynomials---given by a list of coefficients in binary---can be computed to a given accuracy by a ... Acknowledgments I am grateful to Paul Beame

*and*Yuval Filmus

*for*useful discussions,

*and*to anonymous referees

*for*helpful suggestions. ...

##
###
Page 5971 of Mathematical Reviews Vol. , Issue 94j
[page]

1994
*
Mathematical Reviews
*

Summary: “We investigate small-

*depth**threshold**circuits**for**iter*- ated*multiplication**and*related problems. ... This can be compared to the best known construction, which uses four levels of*threshold*gates (but no AC°-circuitry). Similarly, we design small-*depth**circuits**for*powering,*division**and*logarithm. ...##
###
On Defining Integers And Proving Arithmetic Circuit Lower Bounds

2009
*
Computational Complexity
*

X k

doi:10.1007/s00037-009-0260-x
fatcat:lla4pzno45hgzm5pgz6cceqb44
*and*n k=1 1 k X k of exp*and*log, respectively, can be computed by arithmetic*circuits*of size polynomial in log n (allowing*divisions*). ... We prove that if there are arithmetic*circuits*of size polynomial in n*for*computing the permanent of n by n matrices, then τ (n!) is polynomially bounded in log n. ... I thank them, as well as Emmanuel Jeandel*and*Emanuele Viola,*for*useful comments. ...##
###
On defining integers in the counting hierarchy and proving lower bounds in algebraic complexity
[article]

2006
*
Electronic colloquium on computational complexity
*

*circuits*of size polynomial in log n (allowing

*divisions*). ... We prove that if there are arithmetic

*circuits*

*for*computing the permanent of n by n matrices having size polynomial in n, then τ (n!) is polynomially bounded in log n. ... [14] on

*uniform*bounded-

*depth*

*threshold*

*circuits*

*for*

*division*

*and*

*iterated*

*multiplication*of integers. Proof. ...

##
###
Quantum Circuits with Unbounded Fan-out
[article]

2004
*
arXiv
*
pre-print

, mod[q],

arXiv:quant-ph/0208043v3
fatcat:j3b7tuwqnzaarn63bfnfnorpxy
*And*, Or, majority,*threshold*[t], exact[q],*and*Counting. ...*Constant*-*depth*polynomial-size quantum*circuits*with bounded fan-in*and*unbounded fan-out over a fixed basis (denoted by QNCf^0) can approximate with polynomially small error the following gates: parity ... Acknowledgements I would like to thank Harry Buhrman, Hartmut Klauck,*and*Hein Röhrig from Centrum voor Wiskunde en Informatica in Amsterdam,*and*Frederic Green from Clark University in Worcester*for*plenty ...##
###
On the Complexity of Some Problems on Groups Input as Multiplication Tables

2001
*
Journal of computer and system sciences (Print)
*

Finally, we examine the implications of our results

doi:10.1006/jcss.2001.1764
fatcat:7sicpde6rzf7heo3s5gvnksywu
*for*the complexity of*iterated**multiplication*, powering,*and**division*of integers in the context of the recent results of Chiu, Davida,*and*Litow*and*... cyclicity*and*nilpotency can each be tested in FOLL 5 L. ... In addition, the authors thank Eric Allender*and*Bill Hesse*for*permission to allude to results from the forthcoming [1, 2, 21]*and**for*several helpful discussions. ...##
###
Permanent does not have succinct polynomial size arithmetic circuits of constant depth

2013
*
Information and Computation
*

We show that over fields of characteristic zero there does not exist a polynomial p(n)

doi:10.1016/j.ic.2012.10.013
fatcat:t6v6fd4v2zdwxbpxy3m3rf3uuq
*and*a*constant*-free succinct arithmetic*circuit*family {Φn} using*division*by*constants*1 , where Φn has size at most ... p(n)*and**depth*O(1), such that Φn computes the n × n permanent. ... We thank Pavel Hrubeš*for*pointing out to us that without*division*gates a lower bound can be obtained*for*succinct*circuits*of*constant**depth*by a reduction to the Razborov-Smolensky lower bound. ...##
###
Permanent Does Not Have Succinct Polynomial Size Arithmetic Circuits of Constant Depth
[chapter]

2011
*
Lecture Notes in Computer Science
*

We show that over fields of characteristic zero there does not exist a polynomial p(n)

doi:10.1007/978-3-642-22006-7_61
fatcat:tjfzx3b6sngjzcyhqpmrdwcmqi
*and*a*constant*-free succinct arithmetic*circuit*family {Φn} using*division*by*constants*1 , where Φn has size at most ... p(n)*and**depth*O(1), such that Φn computes the n × n permanent. ... We thank Pavel Hrubeš*for*pointing out to us that without*division*gates a lower bound can be obtained*for*succinct*circuits*of*constant**depth*by a reduction to the Razborov-Smolensky lower bound. ...##
###
On TC0, AC0, and Arithmetic Circuits

2000
*
Journal of computer and system sciences (Print)
*

One way to define #AC 0 is as the class of functions computed by

doi:10.1006/jcss.1999.1675
fatcat:7wrl4jiwqrh37j5lbitrok3wgq
*constant*-*depth*polynomial-size arithmetic*circuits*of unbounded fan-in addition*and**multiplication*gates. ... by NSF grants CCR-9509603*and*CCR-9734918. ... Acknowledgments We would like to thank Richard Bumby, David Mix Barrington, Pierre McKenzie, Denis Therien, Noam Nisan*and*Dieter van Melkebeek*for*discussions*and*suggestions on the material. ...##
###
Low-Depth Uniform Threshold Circuits and the Bit-Complexity of Straight Line Programs
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present improved

doi:10.1007/978-3-662-44465-8_2
fatcat:wh23sqqb35dolkokrmqkxc5m24
*uniform*TC 0*circuits**for**division*, matrix powering,*and*related problems, where the improvement is in terms of "majority*depth*" (as studied by Maciel*and*Thérien). ... As a corollary, we obtain improved bounds on the complexity of certain problems involving arithmetic*circuits*, which are known to lie in the counting hierarchy. ... Acknowledgments The first author acknowledges the support of NSF grants CCF-0832787*and*CCF-1064785. ...##
###
Lower Bounds Against Weakly-Uniform Threshold Circuits

2013
*
Algorithmica
*

This strengthens the results by Allender [All99] (

doi:10.1007/s00453-013-9823-y
fatcat:qhysc73akvgzjgzdxl5d5ymula
*for**uniform*TC 0 )*and*by Jansen*and*Santhanam [JS11] (*for*weakly-*uniform*arithmetic*circuits*of*constant**depth*). ... The main result of [JS11] is that Permanent does not have succinct polynomial-size arithmetic*circuits*of*constant**depth*, where arithmetic*circuits*have unbounded fan-in addition*and**multiplication*gates ... We also thank the reviewers*for*comments*and*suggestions that improved the exposition of the paper. ...
« Previous

*Showing results 1 — 15 out of 5,757 results*