scholarly journals On uniform recurrence of a direct product

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Pavel Vadimovich Salimov
Keyword(s):  
Fixed Points ◽  
Direct Product ◽  
Special Issue ◽  
Infinite Word ◽  
International Audience ◽  
Bounded Gaps ◽  
Recurrent Word

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience The direct product of two words is a naturally defined word on the alphabet of pairs of symbols. An infinite word is uniformly recurrent if each its subword occurs in it with bounded gaps. An infinite word is strongly recurrent if the direct product of it with each uniformly recurrent word is also uniformly recurrent. We prove that fixed points of the expanding binary symmetric morphisms are strongly recurrent. In particular, such is the Thue-Morse word.

scholarly journals Special Issue on Visualisations in Historical Linguistics: Introduction

2020 ◽  
Vol Special issue on... ◽  
Author(s):  
Benjamin Molineaux ◽  
Bettelou Los ◽  
Martti Mäkinen
Keyword(s):  
Historical Linguistics ◽  
Data Visualisation ◽  
Complex Materials ◽  
Special Issue ◽  
The Core ◽  
Methodological Research ◽  
International Audience ◽  
Introductory Paper ◽  
The Individual ◽  
Historical Periods

International audience The advent of ever-larger and more diverse historical corpora for different historical periods and linguistic varieties has led to the impossibility of obtaining simple, direct-and yet balancedrepresentations of the core patterns in the data. In order to draw insights from heterogeneous and complex materials of this type, historical linguists have begun to reach for a growing number of data visualisation techniques, from the statistical, to the cartographical, the network-based and beyond. An exploration of the state of this art was the objective of a workshop at the 2018 International Conference on English Historical Linguistics, from whence most of the materials of this Special Issue are drawn. This brief introductory paper outlines the background and relevance of this line of methodological research and presents a summary of the individual papers that make up the collection.

scholarly journals Defect Effect of Bi-infinite Words in the Two-element Case

2001 ◽  
Vol Vol. 4 no. 2 ◽  
Author(s):  
Ján Maňuch
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Alphabet ◽  
Infinite Words ◽  
Infinite Word ◽  
The Family ◽  
International Audience ◽  
Necessary And Sufficient ◽  
Primitive Roots ◽  
Element Set

International audience Let X be a two-element set of words over a finite alphabet. If a bi-infinite word possesses two X-factorizations which are not shiftequivalent, then the primitive roots of the words in X are conjugates. Note, that this is a strict sharpening of a defect theorem for bi-infinite words stated in \emphKMP. Moreover, we prove that there is at most one bi-infinite word possessing two different X-factorizations and give a necessary and sufficient conditions on X for the existence of such a word. Finally, we prove that the family of sets X for which such a word exists is parameterizable.

scholarly journals Lyndon factorization of generalized words of Thue

2002 ◽  
Vol Vol. 5 ◽  
Author(s):  
Anton Černý
Keyword(s):  
Infinite Words ◽  
Infinite Word ◽  
International Audience

International audience The i-th symbol of the well-known infinite word of Thue on the alphabet \ 0,1\ can be characterized as the parity of the number of occurrences of the digit 1 in the binary notation of i. Generalized words of Thue are based on counting the parity of occurrences of an arbitrary word w∈\ 0,1\^+-0^* in the binary notation of i. We provide here the standard Lyndon factorization of some subclasses of this class of infinite words.

scholarly journals On the minimal distance of a polynomial code

2011 ◽  
Vol Vol. 13 no. 4 ◽  
Author(s):  
Peter Pal Pach ◽  
Csaba Szabo
Keyword(s):  
Finite Subset ◽  
60Th Birthday ◽  
Theoretical Problem ◽  
Minimal Distance ◽  
Distribution Of Primes ◽  
Special Issue ◽  
Theoretical Methods ◽  
Algorithms And Complexity ◽  
International Audience ◽  
Special Case

special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity International audience For a polynomial f(x) is an element of Z(2)[x] it is natural to consider the near-ring code generated by the polynomials f circle x, f circle x(2) ,..., f circle x(k) as a vectorspace. It is a 19 year old conjecture of Gunter Pilz that for the polynomial f (x) - x(n) broken vertical bar x(n-1) broken vertical bar ... broken vertical bar x the minimal distance of this code is n. The conjecture is equivalent to the following purely number theoretical problem. Let (m) under bar = \1, 2 ,..., m\ and A subset of N be an arbitrary finite subset of N. Show that the number of products that occur odd many times in (n) under bar. A is at least n. Pilz also formulated the conjecture for the special case when A = (k) under bar. We show that for A = (k) under bar the conjecture holds and that the minimal distance of the code is at least n/(log n)(0.223). While proving the case A = (k) under bar we use different number theoretical methods depending on the size of k (respect to n). Furthermore, we apply several estimates on the distribution of primes.

scholarly journals The extended equivalence and equation solvability problems for groups

2011 ◽  
Vol Vol. 13 no. 4 ◽  
Author(s):  
Gabor Horvath ◽  
Csaba Szabo
Keyword(s):  
Polynomial Time ◽  
Equivalence Problem ◽  
Nilpotent Groups ◽  
60Th Birthday ◽  
Special Issue ◽  
Algorithms And Complexity ◽  
International Audience ◽  
Solvability Problem ◽  
Np Complete ◽  
Equation Solvability

special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity International audience We prove that the extended equivalence problem is solvable in polynomial time for finite nilpotent groups, and coNP-complete, otherwise. We prove that the extended equation solvability problem is solvable in polynomial time for finite nilpotent groups, and NP-complete, otherwise.

scholarly journals Separating the k-party communication complexity hierarchy: an application of the Zarankiewicz problem

2011 ◽  
Vol Vol. 13 no. 4 ◽  
Author(s):  
Thomas P. Hayes
Keyword(s):  
Positive Integer ◽  
Open Problem ◽  
Communication Complexity ◽  
60Th Birthday ◽  
Equal Size ◽  
Special Issue ◽  
Algorithms And Complexity ◽  
International Audience ◽  
Zarankiewicz Problem ◽  
Complexity Hierarchy

special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity International audience For every positive integer k, we construct an explicit family of functions f : \0, 1\(n) -\textgreater \0, 1\ which has (k + 1) - party communication complexity O(k) under every partition of the input bits into k + 1 parts of equal size, and k-party communication complexity Omega (n/k(4)2(k)) under every partition of the input bits into k parts. This improves an earlier hierarchy theorem due to V. Grolmusz. Our construction relies on known explicit constructions for a famous open problem of K. Zarankiewicz, namely, to find the maximum number of edges in a graph on n vertices that does not contain K-s,K-t as a subgraph.

scholarly journals Grammatical compression: compressed equivalence and other problems

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Alberto Bertoni ◽  
Roberto Radicioni
Keyword(s):  
Strategic Games ◽  
Special Issue ◽  
Ability To Work ◽  
Inclusion Problems ◽  
Polynomial Time Algorithms ◽  
Straight Line ◽  
International Audience ◽  
Context Free ◽  
Compressed Data ◽  
Straight Line Programs

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience In this work, we focus our attention to algorithmic solutions for problems where the instances are presented as straight-line programs on a given algebra. In our exposition, we try to survey general results by presenting some meaningful examples; moreover, where possible, we outline the proofs in order to give an insight of the methods and the techniques. We recall some recent results for the problem PosSLP, consisting of deciding if the integer defined by a straight-line program on the ring Z is greater than zero; we discuss some implications in the areas of numerical analysis and strategic games. Furthermore, we propose some methods for reducing Compressed Word Problem from an algebra to another; reductions from trace monoids to the semiring of nonnegative integers are exhibited and polynomial time algorithms for compressed equivalence in monoids related to Dyck reductions are shown. Finally, we consider inclusion problems for context-free languages, proving how in some cases efficient algorithms for these problems benefit from the ability to work with compressed data.

scholarly journals Tag-systems for the Hilbert curve

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Patrice Séébold
Keyword(s):  
Hilbert Space ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Finite Approximations ◽  
Infinite Word ◽  
International Audience ◽  
Filling Curve

International audience Hilbert words correspond to finite approximations of the Hilbert space filling curve. The Hilbert infinite word H is obtained as the limit of these words. It gives a description of the Hilbert (infinite) curve. We give a uniform tag-system to generate automatically H and, by showing that it is almost cube-free, we prove that it cannot be obtained by simply iterating a morphism.

scholarly journals Noneffective Regularity of Equality Languages and Bounded Delay Morphisms

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Juhani Karhumaki ◽  
Aleksi Saarela
Keyword(s):  
Special Issue ◽  
Bounded Delay ◽  
International Audience

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience We give an instance of a class of morphisms for which it is easy to prove that their equality set is regular, but its emptiness is still undecidable. The class is that of bounded delay 2 morphisms.

scholarly journals Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Iliya Bouyukliev ◽  
Veerle Fack ◽  
Joost Winne
Keyword(s):  
Fixed Points ◽  
Hadamard Matrices ◽  
Dual Codes ◽  
International Audience

International audience Before this work, at least 762 inequivalent Hadamard matrices of order 36 were known. We found 7238 Hadamard matrices of order 36 and 522 inequivalent [72,36,12] double-even self-dual codes which are obtained from all 2-(35,17,8) designs with an automorphism of order 3 and 2 fixed points and blocks.

Sign in / Sign up

Export Citation Format

Share Document