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k-Subgraph Isomorphism on AC0 Circuits

2010
*
Computational Complexity
*

In this paper, we study the

doi:10.1007/s00037-010-0288-y
fatcat:xnhxmciuhrdtvcrlx7x3w4gtyi
*complexity*of the k-subgraph isomorphism problem on constant-depth*circuits*. ... the constant-depth*circuit**complexity*for detecting a pattern H (of a fixed size k) of O(n t+1 log n) where t is the treewidth of H. ... Suppose that constant-depth*circuits*of size O(n t ) compute HypClique n ,k , where t = s − 2k s / k . ...##
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On the (Non) NP-Hardness of Computing Circuit Complexity

2015
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Computational Complexity Conference
*

The Minimum

doi:10.4230/lipics.ccc.2015.365
dblp:conf/coco/MurrayW15
fatcat:6fqqwrfaybfeho2yg4dccg75ay
*Circuit*Size Problem (MCSP) is: given the truth table of a Boolean function f and a size parameter k, is the*circuit**complexity*of f at most k? ... We also consider the nondeterministic generalization of MCSP: the Nondeterministic Minimum*Circuit*Size Problem (NMCSP), where one wishes to compute the nondeterministic*circuit**complexity*of a given function ... A simple lemma on the*circuit**complexity*of substrings We also use the fact that for any string T , the*circuit**complexity*of an arbitrary substring of T can be bounded via the*circuit**complexity*of T ...##
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Bounded-width polynomial-size Boolean formulas compute exactly those functions in AC0

1994
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Information Processing Letters
*

We show that the

doi:10.1016/0020-0190(94)00036-0
fatcat:ynkaubckofhhzmyjhkadnkehx4
*complexity*classes*AC0*and NC' consist exactly of, respectively, constant and O(log n) width polynomial-size Boolean formulas. ... Introduction The*complexity*classes AC? and NC' and their modifications are well studied in the literature. For example, Furst et al. [4] and independently Ajtai [ 1 ] proved that*AC0*# NC'. ... Definitions In this section we review some of the basic notions from Boolean*circuit**complexity*(for more details see, for example, [ 61 and [ 31). ...##
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Patterns hidden from simple algorithms

2011
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Communications of the ACM
*

More things appear random to simpler, or resource-limited, algorithms than to

doi:10.1145/1924421.1924445
fatcat:j4e276ibyjco7d4muo2ekyzwai
*complex*, powerful, algorithms. And why should we care? Because randomness is a key resource in computation. ... Only recently, Bazzi [1] resolved a special case of the conjecture (for the case of*AC0*functions corresponding to depth 2*circuits*, or "DNF formulae"). ...*AC0*functions are those whose input-output behavior can be described by a Boolean logic*circuit*consisting n input wires and polynomially many NOT gates and AND and OR gates of arbitrary fan-in. ...##
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Algorithms for Circuits and Circuits for Algorithms

2014
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2014 IEEE 29th Conference on Computational Complexity (CCC)
*

The title of this paper is meant to highlight an emerging duality between two fundamental topics in algorithms and

doi:10.1109/ccc.2014.33
dblp:conf/coco/Williams14
fatcat:t2irb2av2bcb5hzfi2dxkrsvqu
*complexity*theory. ... Algorithms for*circuits*refers to the design of interesting algorithms which can perform non-trivial*circuit*analysis of some kind, on either a*circuit*or a Boolean function given as a truth table. ... (It is known that SETH implies ETH.) 9*AC0*-SAT: The next more expressive class of*circuits*is*AC0*, with arbitrary constant depth. ...##
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Review—Nonlinear Electrochemical Impedance Spectroscopy

2017
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Journal of the Electrochemical Society
*

*Complex*reactions. ... F,N L (E

*ac0*) = R p,N L (E

*ac0*) + R sol = lim ω→0 Z T [4b] If the actual reaction is a simple electron transfer reaction in the kinetic controlled regime, then the

*complex*plane plot of the impedance ...

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Effect of potential drifts and ac amplitude on the electrochemical impedance spectra

2011
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Electrochimica Acta
*

It is shown that if the data were to be analyzed without validation by KKT, it can lead to incorrect choice of reaction mechanism or equivalent

doi:10.1016/j.electacta.2010.12.007
fatcat:oqith5fajjdrrcri7bx5czhdly
*circuits*. ... V*ac0*= 10 mV(original data) V*ac0*= 10 mV(transformed result) V*ac0*= 100 mV(original data) V*ac0*= 100 mV(transformed result)*Complex*plane plots of impedance spectra for direct dissolution under stable ... Vdrift = 0.01V Vdrift = 0.01V V*ac0*=10 mV (original data) Vac0= 0.1V_KKT V*ac0*=10 mV (transformed result)*Complex*plane plots of impedance spectra for dissolution with one adsorbed intermediate species ...##
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Numerical investigations of solution resistance effects on nonlinear electrochemical impedance spectra

2011
*
Journal of Solid State Electrochemistry
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Electrical

doi:10.1007/s10008-011-1477-6
fatcat:ejdmgwqruvaqvd5s2ci3vwtv6q
*circuits*with negative resistances and capacitances were used to simulate the impedance spectra with data in the second quadrant of the*complex*plane plots [33]. ... Fig. 7 7 shows the*complex*plane plots of impedance for V*ac0*= 10 mV, for various solution resistance values. ...##
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Detection of nonlinearities in electrochemical impedance spectra by Kramers–Kronig Transforms

2015
*
Journal of Solid State Electrochemistry
*

(b)

doi:10.1007/s10008-015-2824-9
fatcat:4xe3dmjtpvgd3pcdkeukk6qu4i
*Complex*plane plots of impedance spectra V*ac0*= 1 mV and 300 mV, inset shows the expanded view of V*ac0*= 300 mV low frequency data. ... (a) Figure captions*Complex*plane plots of impedance spectra V*ac0*= 1 mV and 300 mV. Bode plots of (c) |Z| and (d) Φ at V*ac0*= 300 mV. ...##
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Regular languages in NC1

1992
*
Journal of computer and system sciences (Print)
*

We give several characterizations, in terms of formal logic, semigroup theory, and operations on languages, of the regular languages in the

doi:10.1016/0022-0000(92)90014-a
fatcat:ty7dnkixh5arhkhul52ibdfiee
*circuit**complexity*class AC', thus answering a question of Chandra ... We also obtain logical characterizations for the class of all languages recognized by nonuniform*circuit*families in which mod m gates (where m is not necessarily prime) are permitted. ... Indeed, any regular language in*AC0*can be recognized by a highly uniform*AC0**circuit*family. ...##
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A note on some languages in uniform ACC0

1991
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Theoretical Computer Science
*

ACC" (also called ACC) is the class of languages recognized by

doi:10.1016/0304-3975(91)90357-8
fatcat:xcsxu6vvwbfynfg5mk7em2dbfq
*circuit*families with polynomial size, constant depth, and u? ...*circuit*for L,. This being impossible, we can conclude that no family of*AC0**circuits*exists for L,. ... fan-in two and depth O(Iog n)-see [6] for an overview of*circuit**complexity*theory). ...##
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An analysis of drifts and nonlinearities in electrochemical impedance spectra

2011
*
Electrochimica Acta
*

The inset shows the low frequency impedance for V

doi:10.1016/j.electacta.2011.06.112
fatcat:q7r6imtnf5ei5i4eax3leofpay
*ac0*of 200 mV, expanded for clarity X V*ac0*= 1 mV V*ac0*= 10 mV V*ac0*= 100 mV V*ac0*= 200 mV Fig. 8 .Fig 9 . 89*Complex*plane plots of impedance spectra ... The charge stabilized are presented as*complex*plane plots infig. 8. Again, the impedance values for V*ac0*= 1 mV and 10 mV are identical. ...##
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On uniformity within NC1

1990
*
Journal of computer and system sciences (Print)
*

We show that these two notions are equivalent, leading to a natural notion of uniformity for low-level

doi:10.1016/0022-0000(90)90022-d
fatcat:zdlwqu25tnh6rbht7wd264jfe4
*circuit**complexity*classes. ... In order to study*circuit**complexity*classes within NC' in a uniform setting, we need a uniformity condition which is more restrictive than those in common use. ... We will now define our basic*circuit**complexity*classes in their non-uniform versions. ...##
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Queries with arithmetical constraints

1997
*
Theoretical Computer Science
*

We first consider the data

doi:10.1016/s0304-3975(96)00194-6
fatcat:2l24uv556reahd6xv2u57wxgqu
*complexity*of first-order queries. ... We prove in particular that linear queries can be evaluated in*AC0*over finite integer databases, and in NC' over linear constraint databases. This improves previously known bounds. ... We consider classical*complexity*classes based on Turing machines such as LOGSPACE and PTIME, classes based on Boolean*circuits*, with AND, OR, and NEG gates, such as*AC0*with constant depth, a polynomial ...##
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Fusion trees can be implemented with AC0 instructions only

1999
*
Theoretical Computer Science
*

The

doi:10.1016/s0304-3975(98)00172-8
fatcat:so6qb5xhijetnk3vjth7h37324
*AC0*instructions used are not all available on today's computers. @ 1999-Elsevier Science B.V. ... Addressing a problem of Fredman and Willard, we implement fusion trees in deterministic linear space using*AC0*instructions only. ... Fredman and Willard point out that multiplication is not an*AC0*instruction, that is, there are no*circuits*for multiplication of constant depth and of size (number of gates) polynomial in the word length ...
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