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Symmetric Arithmetic Circuits
[article]

2021
*
arXiv
*
pre-print

We introduce

arXiv:2002.06451v2
fatcat:unqswydznrdilitkbpza5gfsdu
*symmetric**arithmetic**circuits*, i.e.*arithmetic**circuits*with a natural symmetry restriction. ... We establish unconditional exponential lower bounds on the size of any*symmetric**circuit*for computing the permanent. ... Though*symmetric**arithmetic**circuits*have not previously been studied,*symmetric*Boolean*circuits*have [15, 23, 2, 24] . ...##
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Symmetric Arithmetic Circuits

2020
*
International Colloquium on Automata, Languages and Programming
*

We introduce

doi:10.4230/lipics.icalp.2020.36
dblp:conf/icalp/DawarW20
fatcat:hjjh3sbiwbcuzdakr2cak5v44m
*symmetric**arithmetic**circuits*, i.e.*arithmetic**circuits*with a natural symmetry restriction. ... In contrast, we show that there are polynomial-size*symmetric**circuits*for computing the determinant over fields of characteristic zero. ... Though*symmetric**arithmetic**circuits*have not previously been studied,*symmetric*Boolean*circuits*have [13, 20, 2] . ...##
###
Ultra-Low Leakage Arithmetic Circuits Using Symmetric and Asymmetric FinFETs

2013
*
Journal of Electrical and Computer Engineering
*

We are examining different configurations and

doi:10.1155/2013/454392
fatcat:umbmxbytuzautjlhg5mirxxwbu
*circuit*topologies for*arithmetic*components such as adder and compressor*circuits*using both*symmetric*and asymmetric work-function FinFETs. ... Based on extensive characterization data, for the carry generation of a mirror full adder using*symmetric*devices, both leakage current and delay are decreased by 25% and 50%, respectively, compared to ... The goal of this paper is to develop*circuit*topologies and configurations that lead to high-performance low leakage*arithmetic*components using*symmetric*four-terminal FinFETs. ...##
###
Symmetric Arithmetic Circuits
[article]

2020

We introduce

doi:10.17863/cam.56098
fatcat:zlpxdqyccbgnvgqws7gmo77lsi
*symmetric**arithmetic**circuits*, i.e.*arithmetic**circuits*with a natural symmetry restriction. ... In contrast, we show that there are polynomial-size*symmetric**circuits*for computing the determinant over fields of characteristic zero. ... Though*symmetric**arithmetic**circuits*have not previously been studied,*symmetric*Boolean*circuits*have [14, 21, 2] . ...##
###
On the Complexity of Symmetric Polynomials

2018
*
Innovations in Theoretical Computer Science
*

Furthermore, we study the complexity of testing whether a function is

doi:10.4230/lipics.itcs.2019.47
dblp:conf/innovations/BlaserJ19
fatcat:lq7xln6rwvcvnby7ggqxzinlry
*symmetric*. For polynomials, this question is equivalent to*arithmetic**circuit*identity testing. ... As a corollary of this result, we show that if VP = VNP then there exist*symmetric*polynomial families which have super-polynomial*arithmetic*complexity. ... Given an*arithmetic**circuit*C computing the polynomial f (x 1 , x 2 , . . . , x n ), check if f is a*symmetric*polynomial? ...##
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Arithmetic optimization for custom instruction set synthesis

2009
*
2009 IEEE 7th Symposium on Application Specific Processors
*

Unlike earlier work (e.g., Three Greedy Approach [1], [2]) our approach does not require any prior knowledge about the functionality of the

doi:10.1109/sasp.2009.5226336
dblp:conf/sasp/VermaZBI09
fatcat:zfwct4kis5e6jcrisn47net3gi
*circuit*. ... The proposed technique automatically infers the use of carry-save*arithmetic*, when appropriate, and suppresses its use when unfavorable. ... Logic synthesis techniques work quite well for finite state machines and control dominated*circuits*, but are generally ineffective for*arithmetic**circuits*, meaning that there is a large gap between*arithmetic*...##
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Affine projections of symmetric polynomials

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

We refer to this model as the

doi:10.1016/s0022-0000(02)00021-1
fatcat:mm7gujcfbja23mddrnk3z4gu5e
*symmetric*model. This new model is related to standard models of*arithmetic**circuits*, especially to depth-3*circuits*. ... In this paper, we introduce a new model for computing polynomials-a depth-2*circuit*with a*symmetric*gate at the top and plus gates at the bottom, i.e. the*circuit*computes a*symmetric*function in linear ... Definition 2. 2 . 2 A depth-2*symmetric**arithmetic**circuit*is a layered graph with two levels. ...##
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Data-Width-Driven Power Gating of Integer Arithmetic Circuits

2012
*
2012 IEEE Computer Society Annual Symposium on VLSI
*

We deploy coarse-grain power gating in 32-bit integer

doi:10.1109/isvlsi.2012.59
dblp:conf/isvlsi/HoangL12
fatcat:euujngraznbfzhn6lyqq6sc3a4
*arithmetic**circuits*that frequently will operate on narrow-width data. ... When performing narrow-width computations, power gating of unused*arithmetic**circuit*portions can significantly reduce leakage power. ... First we consider the*arithmetic**circuit*netlist as a graph. ...##
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Symmetric Determinantal Representation of Weakly-Skew Circuits

2011
*
Symposium on Theoretical Aspects of Computer Science
*

We deploy algebraic complexity theoretic techniques for constructing

doi:10.4230/lipics.stacs.2011.543
dblp:conf/stacs/GrenetKKP11
fatcat:lkeemh3dnbcjloosj7nigiongu
*symmetric*determinantal representations of weakly-skew*circuits*, which include formulas. ... formula or a weakly-skew*circuit*). ... We thank Meena Mahajan for pointing out [13] and sketching the construction of a*symmetric*determinant of size O(n 3 ) from a determinant of size n. ...##
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Page 1118 of Mathematical Reviews Vol. , Issue 87b
[page]

1987
*
Mathematical Reviews
*

This paper presents a theoretical approach to a new class of nonbinary

*arithmetic*AN codes using*symmetric*R-ary expres- sions and Lee-type*arithmetic*distance. ... “Following the introductory descriptions of*symmetric*R-ary expressions, some important properties of the*arithmetic*distance and the error correctabilities of the codes are discussed. ...##
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Lower bounds on arithmetic circuits via partial derivatives

1996
*
Computational Complexity
*

In this paper we describe a new technique for obtaining lower bounds on restriced classes of nonmonotone

doi:10.1007/bf01294256
fatcat:ro7foiksize4lb33vidkglz6oy
*arithmetic**circuits*. ... We use the technique to obtain new lower bounds for computing*symmetric*polynomials and iterated matrix prod- ... This sad state of affairs is essentially also true for*arithmetic**circuits*, a natural model for computing*arithmetic*functions (see e.g. [9] ). ...##
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Smaller ACC0 Circuits for Symmetric Functions
[article]

2021
*
arXiv
*
pre-print

That is, depth-3 CC^0

arXiv:2107.04706v1
fatcat:qc6zzlxpovfyxhkndnvo2ng3uy
*circuits*can compute any*symmetric*function in subexponential size. ... We construct MOD_m*circuits*computing*symmetric*functions with non-prime power m, with size-depth tradeoffs that beat the longstanding lower bounds for AC^0[m]*circuits*for prime power m. ... In order to apply the elementary*symmetric*polynomials, our construction also involves*arithmetic**circuits*over prime fields. ...##
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Page 652 of Mathematical Reviews Vol. , Issue 88b
[page]

1988
*
Mathematical Reviews
*

N>0O such that every d-p(n)

*symmetric**circuit*with n > N inputs has its corresponding subset including or ... A function n+ K(n) C {0,1,..., n} is*circuit*-definable if there exists a sequence C,, of d-p(n)*symmetric**circuits*of n inputs (n € N) for some fixed polynomial p and a constant d, such that the cor- responding ...##
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Faster Bootstrapping of FHE over the integers with large prime message space
[article]

2019
*
IACR Cryptology ePrint Archive
*

In this paper, we express this double modulo reduction

dblp:journals/iacr/LianHCW19
fatcat:o5avzofofngjfmjrqplz6metjm
*circuit*as a*arithmetic**circuit*of degree at most θ 2 log 2 θ/2, with O(θ log 2 θ) multiplication gates, where θ = λ log λ and λ is the security parameter ... Bootstrapping of FHE over the integer with large message is a open problem, which is to evaluate double modulo (c mod p) mod Q*arithmetic*homomorphically for large Q. ... The following lemma 1 states Ben-or's observation that multilinear*symmetric*polynomials can be computed by restricted depth-3*arithmetic**circuits*that perform interpolation. ...##
###
Page 2098 of Mathematical Reviews Vol. , Issue 80E
[page]

1980
*
Mathematical Reviews
*

Information and communication,

*circuits*Author’s summary: “An*arithmetic*-logical device is described which secures effective execution of*arithmetic*and logical opera- tions, over fields of bits of arbitrary ... Authors’ summary: “We show that it is possible to shorten calcu- lations in the structural synthesis of RLC-*circuits*whose conduc- tivity graphs are*symmetric*. ...
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