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Parallel complexity of iterated morphisms and the arithmetic of small numbers
[chapter]

1992
*
Lecture Notes in Computer Science
*

We improve several upper bounds to

doi:10.1007/3-540-55808-x_21
fatcat:slhaxrzckzgkhhl6basphzgiqm
*the**complexity**of**the*membership problem for languages de ned by*iterated**morphisms*(D0L systems). ... to T C 0 if*and*only if upper bounds to a*number**of*natural*arithmetic*problems can be improved to T C 0 . 4)*The*general D0L membership problem (*the*D0L system is part*of**the*input) is contained in Cook's ... Acknowledgments We would like to thank*the*following people for many hints*and*helpful discussions: Birgit Jenner, Bernd Kreu ler, Peter Rossmanith, Wojciech Rytter,*and*Thomas Zeugmann. ...##
###
Parameterized complexity of quantum invariants
[article]

2019
*
arXiv
*
pre-print

We give a general fixed parameter tractable algorithm to compute quantum invariants

arXiv:1910.00477v1
fatcat:qzzlabzd4zhezfuw4eux36rb44
*of*links presented by diagrams, whose*complexity*is singly exponential in*the*carving-width (or*the*tree-width)*of**the*... cw,*and*whose components are coloured with g-modules*of*dimension at most N. ... Then, given*the*matrices for*morphisms*f*and*g, we can compute*the*matrix for*morphism*h in O(abc)*arithmetic*operations in R,*and*memory*complexity*O(ab + bc + ac) times*the*size*of*a scalar in R. ...##
###
Adams operations on higher arithmetic K-theory
[article]

2009
*
arXiv
*
pre-print

*The*definition applies to

*the*higher

*arithmetic*K-groups given by Takeda as well as to

*the*groups suggested by Deligne

*and*Soule, by means

*of*

*the*homotopy groups

*of*

*the*homotopy fiber

*of*

*the*regulator ... In this paper it is shown that a slight modification

*of*this chain

*morphism*commutes strictly with

*the*representative

*of*

*the*Beilinson regulator given by Burgos

*and*Wang. ... We follow

*the*conventions

*and*definitions on (co)chain

*complexes*

*and*

*iterated*(co)chain

*complexes*as given in [BKK07, §2] . All (co)chain

*complexes*are

*of*abelian groups. ...

##
###
Adams Operations on Higher Arithmetic K-theory

2010
*
Publications of the Research Institute for Mathematical Sciences
*

It is shown that this chain

doi:10.2977/prims/3
fatcat:7i4bwmvd5vbnnjyt2bhv5puspu
*morphism*commutes strictly with*the*representative*of**the*Beilinson regulator given by Burgos*and*Wang. ...*The*definition applies to*the*higher*arithmetic*K-groups given by Takeda as well as to*the*groups suggested by Deligne*and*Soulé, by means*of**the*homotopy groups*of**the*homotopy fiber*of**the*regulator ...*of*hermitian metrics on*the*Koszul*complex*. ...##
###
Page 3478 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

Rios, Strong normalization

*of*substitutions (209-217); 68 COMPUTER SCIENCE 3478 Carsten Damm, Markus Holzer*and*Klaus-Jérn Lange,*Parallel**complexity**of**iterated**morphisms**and**the**arithmetic**of**small**numbers*... Zucker, Theory*of*computation over stream algebras,*and*its applications (62-80); Osamu Watan- abe [Osamu Watanabe’], On*the**complexity**of**small*description*and*related topics (82-94); Juraj Wiedermann ...##
###
Categorial Compositionality III: F-(co)algebras and the Systematicity of Recursive Capacities in Human Cognition

2012
*
PLoS ONE
*

in a list-implies

doi:10.1371/journal.pone.0035028
pmid:22514704
pmcid:PMC3325926
fatcat:b47temdl5bejlb57o4mhgp75de
*the*capacity for certain others-finding*the*largest*number*, given knowledge*of**number*order). ... In particular,*the*link between*number**and*language does not depend on recursion, as such, but on*the*underlying functor on which*the*group*of*recursive capacities is based. ... T, where root : (op,l,r).Sop,l,rT,*and*O~fz,{, Ã ,=g is*the*set*of**arithmetic*operators. Here,*the*set*of**numbers*N includes*the*reals. ...##
###
Deformation Techniques for Efficient Polynomial Equation Solving

2000
*
Journal of Complexity
*

*The*underlying algorithm is highly efficient, i.e., polynomial in

*the*syntactic description

*of*

*the*input

*and*

*the*following geometric invariants:

*the*

*number*

*of*solutions

*of*a typical parameter instance ...

*and*

*the*degree

*of*

*the*polynomials occurring in

*the*output. ... )

*the*degree

*of*

*the*output equation may be

*small*

*and*that this degree influences stronlgy

*the*

*complexity*

*of*

*the*algorithm. ...

##
###
Parallelizing Imperative Functional Programs: the Vectorization Monad

1996
*
Journal of symbolic computation
*

Traditionally a vectorizing compiler matches

doi:10.1006/jsco.1996.0031
fatcat:3algmvszvva5vgub454lwjsk6e
*the**iterative*constructs*of*a program against a set*of*predefined templates. ... This technique enables*the*elimination*of*template matching from a vectorizing compiler,*and**the*proof*of**the*safety*of*vectorization can be performed by a type inference mechanism. ... is*the**number**of**iterations**of**the*for-loop. ...##
###
The large structures of Grothendieck founded on finite order arithmetic
[article]

2014
*
arXiv
*
pre-print

We formalize

arXiv:1102.1773v4
fatcat:a7rpq4punjg7xoo5m7nka4dtve
*the*practical insight by founding*the*theorems*of*EGA*and*SGA, plus derived categories, at*the*level*of*finite order*arithmetic*. ... Such large-structure tools*of*cohomology as toposes*and*derived categories stay close to*arithmetic*in practice, yet existing foundations for them go beyond*the*strong set theory ZFC. ... Acknowledgments It is a pleasure to thank people who contributed ideas to this work, which does not mean any*of*them shares any given viewpoint here. ...##
###
Numeration Systems: a Link between Number Theory and Formal Language Theory
[article]

2012
*
arXiv
*
pre-print

We discuss

arXiv:1204.5887v1
fatcat:xoju4renerhqzcr245luz7klye
*the*notion*of*numeration systems, recognizable sets*of*integers*and*automatic sequences. We briefly sketch some results about transcendence related to*the*representation*of*real*numbers*. ... We survey facts mostly emerging from*the*seminal results*of*Alan Cobham obtained in*the*late sixties*and*early seventies. ... Acknowledgments I would like to thank Boris Adamczewski, Valérie Berthé, Véronique Bruyère, Eric Duchêne, Narad Rampersad for*the*careful reading*of*a first draft*of*this paper. ...##
###
Numeration Systems: A Link between Number Theory and Formal Language Theory
[chapter]

2010
*
Lecture Notes in Computer Science
*

We discuss

doi:10.1007/978-3-642-14455-4_6
fatcat:nl3tcpwgcfdfxffsyyvzkeher4
*the*notion*of*numeration systems, recognizable sets*of*integers*and*automatic sequences. We briefly sketch some results about transcendence related to*the*representation*of*real*numbers*. ... We survey facts mostly emerging from*the*seminal results*of*Alan Cobham obtained in*the*late sixties*and*early seventies. ... Acknowledgments I would like to thank Boris Adamczewski, Valérie Berthé, Véronique Bruyère, Eric Duchêne, Narad Rampersad for*the*careful reading*of*a first draft*of*this paper. ...##
###
Book announcements

1990
*
Discrete Applied Mathematics
*

*The*absence

*of*gaps in

*the*crosscap range. A genus-related upper bound on

*the*crosscap

*number*.

*The*genus

*and*crosscap

*number*

*of*

*the*complete graph K7. ... Chapter 6: Geometric Patterns

*of*

*Small*Order: Spectra

*and*Context. Chapter I: Stratification

*and*Normalization. Chapter 8:

*The*Diameter-limited Perception. ...

##
###
Arithmetic characteristic classes of automorphic vector bundles
[article]

2005
*
arXiv
*
pre-print

Then we introduce

arXiv:math/0502085v1
fatcat:a2hqraxx3bb4fky3gjgn2hj2em
*the*notion*of*log-singular hermitian vector bundles, which is a variant*of**the*good hermitian vector bundles introduced by Mumford,*and*we develop*the*theory*of**arithmetic*characteristic ... We first study*the*cohomological properties*of*log-log differential forms, prove a Poincar\'e lemma for them*and*construct*the*corresponding*arithmetic*Chow groups. ... Furthermore, we would like to thank EAGER,*the**Arithmetic*Geometry Network,*the*Newton Institute (Cambridge),*and**the*Institut Henri Poincaré (Paris) for partial support*of*our work. ...##
###
Page 1032 of Mathematical Reviews Vol. , Issue 92b
[page]

1992
*
Mathematical Reviews
*

Madatyan, An estimate

*of**the**number**of*representative sets for a class*of*binary tables (Russian) (pp. 513-522); M. Yu. ...*Parallel*architectures*and*languages Europe. Vol. I.*Parallel*architectures*and*algorithms. Proceedings*of**the*conference held in Eindhoven, June 10-13, 1991. Edited by E. H. L. ...##
###
The dynamical André–Oort conjecture: Unicritical polynomials

2017
*
Duke mathematical journal
*

first complete case

doi:10.1215/00127094-3673996
fatcat:4kpdzanji5exjnhhtudg67nwtq
*of**the*dynamical Andre-Oort phenomenon studied by Baker*and*DeMarco. ... d>2), we classify all*complex*plane curves C with Zariski-dense subsets*of*points (a,b)∈ C, such that both z^d+a*and*z^d+b are simultaneously post-critically finite for a fixed degree d≥ 2. ... One*of**the*main ingredients*of*our article (*and*also*of*all*of**the*above articles) is*the**arithmetic*equidistribution*of**small*points on an algebraic variety (in*the*case*of*P1 , see [BR06, FRL06], in ...
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