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

Carsten Damm, Markus Holzer, Klaus-Jörn Lange
1992 Lecture Notes in Computer Science  
We improve several upper bounds to 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.  ... 
doi:10.1007/3-540-55808-x_21 fatcat:slhaxrzckzgkhhl6basphzgiqm

Parameterized complexity of quantum invariants [article]

Clément Maria
2019 arXiv   pre-print
We give a general fixed parameter tractable algorithm to compute quantum invariants 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.  ... 
arXiv:1910.00477v1 fatcat:qzzlabzd4zhezfuw4eux36rb44

Adams operations on higher arithmetic K-theory [article]

Elisenda Feliu
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.  ... 
arXiv:0906.1488v1 fatcat:xmswyli24rgfnbmhz6x22oazsi

Adams Operations on Higher Arithmetic K-theory

Elisenda Feliu
2010 Publications of the Research Institute for Mathematical Sciences  
It is shown that this chain 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.  ... 
doi:10.2977/prims/3 fatcat:7i4bwmvd5vbnnjyt2bhv5puspu

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

Steven Phillips, William H. Wilson, Olaf Sporns
2012 PLoS ONE  
in a list-implies 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.  ... 
doi:10.1371/journal.pone.0035028 pmid:22514704 pmcid:PMC3325926 fatcat:b47temdl5bejlb57o4mhgp75de

Deformation Techniques for Efficient Polynomial Equation Solving

Joos Heintz, Teresa Krick, Susana Puddu, Juan Sabia, Ariel Waissbein
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.  ... 
doi:10.1006/jcom.1999.0529 fatcat:l2pnj6o4zjao3lezubz43i5csi

Parallelizing Imperative Functional Programs: the Vectorization Monad

JONATHAN M.D. HILL, KEITH M. CLARKE, RICHARD BORNAT
1996 Journal of symbolic computation  
Traditionally a vectorizing compiler matches 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.  ... 
doi:10.1006/jsco.1996.0031 fatcat:3algmvszvva5vgub454lwjsk6e

The large structures of Grothendieck founded on finite order arithmetic [article]

Colin McLarty
2014 arXiv   pre-print
We formalize 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.  ... 
arXiv:1102.1773v4 fatcat:a7rpq4punjg7xoo5m7nka4dtve

Numeration Systems: a Link between Number Theory and Formal Language Theory [article]

Michel Rigo
2012 arXiv   pre-print
We discuss 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.  ... 
arXiv:1204.5887v1 fatcat:xoju4renerhqzcr245luz7klye

Numeration Systems: A Link between Number Theory and Formal Language Theory [chapter]

Michel Rigo
2010 Lecture Notes in Computer Science  
We discuss 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.  ... 
doi:10.1007/978-3-642-14455-4_6 fatcat:nl3tcpwgcfdfxffsyyvzkeher4

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.  ... 
doi:10.1016/0166-218x(90)90074-m fatcat:uhwd4fl3wvcetkvers2zklsbry

Arithmetic characteristic classes of automorphic vector bundles [article]

J. I. Burgos Gil, J. Kramer, U. Kuehn
2005 arXiv   pre-print
Then we introduce 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.  ... 
arXiv:math/0502085v1 fatcat:a2hqraxx3bb4fky3gjgn2hj2em

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

D. Ghioca, H. Krieger, K. D. Nguyen, H. Ye
2017 Duke mathematical journal  
first complete case 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  ... 
doi:10.1215/00127094-3673996 fatcat:4kpdzanji5exjnhhtudg67nwtq
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