References of "Rigo, Michel"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 61 to 80 of 97     1 2 3 4 5     A Decision Problem for Ultimately Periodic Sets in Non-standard Numeration SystemsBell, Jason; Charlier, Emilie ; Fraenkel, Aviezri et alin International Journal of Algebra & Computation (2009), 19Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers ... [more ▼]Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure for this problem, under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language. [less ▲]Detailed reference viewed: 69 (27 ULg) Syndeticity and independent substitutionsDurand, Fabien; Rigo, Michel in Advances in Applied Mathematics (2009), 42We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we de ne the notion of two independent ... [more ▼]We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we de ne the notion of two independent substitutions. Our main result is the following. If a sequence x is generated by two independent substitutions, at least one being of exponential growth, then the factors of x appearing in nitely often in x appear with bounded gaps. As an application, we derive an analogue of Cobham's theorem for two independent substitutions (or abstract numeration systems) one with polynomial growth, the other being exponential. [less ▲]Detailed reference viewed: 43 (11 ULg) Les codes correcteursRigo, Michel Learning material (2009)Qu'on le veuille ou non, nous vivons dans un monde où les informations et les moyens de communication sont omniprésents. Les exemples où se mêlent informatique et télécommunications sont nombreux. Que ce ... [more ▼]Qu'on le veuille ou non, nous vivons dans un monde où les informations et les moyens de communication sont omniprésents. Les exemples où se mêlent informatique et télécommunications sont nombreux. Que ce soit l'Internet, la musique achetée en ligne ou gravée sur CD, les baladeurs de type iPod et autres appareils portables, les supports mémoire de tout type, la photographie numérique, la présence d'ordinateurs de bord sophistiqués dans nos voitures, etc. Sans code correcteur, le CD (implémentant un code correcteur de type Reed-Solomon) et de nombreux autres produits n'auraient probablement jamais connu le succès ! [less ▲]Detailed reference viewed: 57 (11 ULg) Abstract numeration systems on bounded languages and multiplication by a constantCharlier, Emilie ; Rigo, Michel ; Steiner, Wolfgangin INTEGERS: Electronic Journal of Combinatorial Number Theory (2008), 8(1-A35), 1-19A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems ... [more ▼]A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with at least three letters, we show that multiplication by an integer $\lambda\ge2$ does not preserve $S$-recognizability, meaning that there always exists a $S$-recognizable set $X$ such that $\lambda X$ is not $S$-recognizable. The main tool is a bijection between the representation of an integer over a bounded language and its decomposition as a sum of binomial coefficients with certain properties, the so-called combinatorial numeration system. [less ▲]Detailed reference viewed: 41 (7 ULg) A decision problem for ultimately periodic sets in non-standard numeration systemsCharlier, Emilie ; Rigo, Michel in Actes des Journées Montoises d'Informatique Théorique (2008)Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of ... [more ▼]Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language. [less ▲]Detailed reference viewed: 23 (2 ULg) Combinatorics, Automata and Number Theory 2006Berthé, Valérie; Lecomte, Pierre ; Rigo, Michel in Theoretical Computer Science (2008), 391Detailed reference viewed: 18 (5 ULg) Cubic Pisot Unit Combinatorial GamesDuchêne, Eric; Rigo, Michel in Monatshefte für Mathematik (2008), 155Generalized Tribonacci morphisms are de ned on a three letters alphabet and generate the so-called generalized Tribonacci words. We present a family of combinatorial removal games on three piles of tokens ... [more ▼]Generalized Tribonacci morphisms are de ned on a three letters alphabet and generate the so-called generalized Tribonacci words. We present a family of combinatorial removal games on three piles of tokens whose set of P-positions is coded exactly by these generalized Tribonacci words. To obtain this result, we study combinatorial properties of these words like gaps between consecutive identical letters or recursive de nitions of these words. Beta-numeration systems are then used to show that these games are tractable, i.e., deciding whether a position is a P-position can be checked in polynomial time. [less ▲]Detailed reference viewed: 26 (2 ULg) A morphic approach to combinatorial games : the Tribonacci caseDuchêne, Eric; Rigo, Michel in Theoretical Informatics and Applications. Informatique Théorique et Applications (2008), 42We propose a variation of Wythoff's game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game ... [more ▼]We propose a variation of Wythoff's game on three piles of tokens, in the sense that the losing positions can be derived from the Tribonacci word instead of the Fibonacci word for the two piles game. Thanks to the corresponding exotic numeration system built on the Tribonacci sequence, deciding whether a game position is losing or not can be computed in polynomial time. [less ▲]Detailed reference viewed: 20 (2 ULg) Syntactictal and automatic properties of sets of polynomials over finite fieldsRigo, Michel in Finite Fields & Their Applications (2008), 42Syntactical properties of representations of integers in various number systems are well-known and have been extensively studied. In this paper, we transpose the notion of recognizable set of integers ... [more ▼]Syntactical properties of representations of integers in various number systems are well-known and have been extensively studied. In this paper, we transpose the notion of recognizable set of integers into the framework of the polynomial ring over a finite field F. We define B-recognizable sets of polynomials over F and consider their first properties. [less ▲]Detailed reference viewed: 17 (2 ULg) A Decision Problem for Ultimately Periodic Sets in Non-standard Numeration SystemsCharlier, Emilie ; Rigo, Michel in Lecture Notes in Computer Science (2008), 5162Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of ... [more ▼]Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language. [less ▲]Detailed reference viewed: 23 (11 ULg) La matrice cachée de GoogleRigo, Michel Learning material (2008)Inutile de le présenter : Google est le moteur de recherche le plus connu et le plus utilisé au monde. Mais comment les concepteurs de Google font-ils pour classer les milliers de pages se rapportant à un ... [more ▼]Inutile de le présenter : Google est le moteur de recherche le plus connu et le plus utilisé au monde. Mais comment les concepteurs de Google font-ils pour classer les milliers de pages se rapportant à un mot-clé donné, de façon telle que les pages les plus représentatives occupent toujours les premières positions du classement ? Ce tour de force repose sur de véritables résultats mathématiques combinant théorie des graphes et algèbre linéaire. [less ▲]Detailed reference viewed: 290 (8 ULg) About frequencies of letters in generalized automatic sequencesNicolay, Samuel ; Rigo, Michel in Theoretical Computer Science (2007), 374(1-3), 25-40We present some asymptotic results about the frequency of a letter appearing in a generalized unidimensional automatic sequence. Next, we study multidimensional generalized automatic sequences and the ... [more ▼]We present some asymptotic results about the frequency of a letter appearing in a generalized unidimensional automatic sequence. Next, we study multidimensional generalized automatic sequences and the corresponding frequencies. (C) 2006 Elsevier B.V. All rights reserved. [less ▲]Detailed reference viewed: 19 (6 ULg) Distribution of additive functions with respect to numeration systems on regular languagesGrabner, Peter J.; Rigo, Michel in Theory of Computing Systems (2007), 40(3), 205-223We study the distribution of values of additive functions related to numeration systems defined via regular languages.Detailed reference viewed: 25 (5 ULg) Odometers on regular languagesBerthé; Rigo, Michel in Theory of Computing Systems (2007), 40(1), 1-31Odometers or "adding machines" are usually introduced in the context of positional numeration systems built on a strictly increasing sequence of integers. We generalize this notion to systems defined on ... [more ▼]Odometers or "adding machines" are usually introduced in the context of positional numeration systems built on a strictly increasing sequence of integers. We generalize this notion to systems defined on an arbitrary infinite regular language. In this latter situation, if (A, <) is a totally ordered alphabet, then enumerating the words of a regular language L over A with respect to the induced genealogical ordering gives a one-to-one correspondence between N and L. In this general setting the odometer is not defined on a set of sequences of digits but on a set of pairs of sequences where the first (resp. the second) component of the pair is an infinite word over A (resp. an infinite sequence of states of the minimal automaton of L). We study some properties of the odometer such as continuity, injectivity, surjectivity, minimality,... We then study some particular cases: we show the equivalence of this new function with the classical odometer built upon a sequence of integers whenever the set of greedy representations of all the integers is a regular language; we also consider substitution numeration systems as well as the connection with beta-numerations. [less ▲]Detailed reference viewed: 25 (5 ULg) special issue dedicated to the tenth Journées montoises d'informatique théorique''Bruyère, Véronique; Rigo, Michel in Discrete Mathematics & Theoretical Computer Science (2007), 9(2), 1Detailed reference viewed: 16 (5 ULg) Pirates informatiques et mathématique modulaireRigo, Michel Learning material (2007)De nos jours, l'envoi de messages secrets requiert la manipulation de nombres ayant plus de cent chiffres décimaux. Nous illustrons une technique cryptographique standard (le RSA) dont la sécurité réside ... [more ▼]De nos jours, l'envoi de messages secrets requiert la manipulation de nombres ayant plus de cent chiffres décimaux. Nous illustrons une technique cryptographique standard (le RSA) dont la sécurité réside dans le fait qu'il est "rapide", sur le plus banal des ordinateurs personnels, de calculer le produit de deux "grands" nombres (cela se compte au pire en secondes), alors que le temps nécessaire pour effectuer l'opération inverse de factorisation prend, dans l'état actuel des connaissances mathématiques, énormément plus de temps (que l'on pourrait estimer en milliards d'années même pour un super-calculateur !). [less ▲]Detailed reference viewed: 63 (6 ULg) On the cost and complexity of the successor functionBerthé, Valérie; Frougny, Christiane; Rigo, Michel et alin Arnoux, P.; Bédaride, N. (Eds.) Proceedings of WORDS 2007 (2007)For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the n-th word ... [more ▼]For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the n-th word of a genealogically ordered language L onto the (n+1)-th word of L. We show that, if the ratio of the number of elements of length n + 1 over the number of elements of length n of the language has a limit b> 1, then the amortized cost of the successor function is equal to b/(b − 1). From this, we deduce the value of the amortized cost for several classes of numeration systems (integer base systems, canonical numeration systems associated with a Parry number, abstract numeration systems built on a rational language, and rational base numeration systems). [less ▲]Detailed reference viewed: 14 (1 ULg) Syntactictal and automatic properties of sets of polynomials over finite fieldsRigo, Michel Conference (2006, October)Detailed reference viewed: 12 (1 ULg) Abstract numeration systems : a survey.Rigo, Michel Conference (2006, August)Detailed reference viewed: 18 (3 ULg) Structural properties of bounded languages with respect to multiplication by a constantCharlier, Emilie ; Rigo, Michel in Actes des Journées Montoises d'Informatique Théorique (2006)We consider the preservation of recognizability of a set of integers after multiplication by a constant for numeration systems built over a bounded language. As a corollary we show that any nonnegative ... [more ▼]We consider the preservation of recognizability of a set of integers after multiplication by a constant for numeration systems built over a bounded language. As a corollary we show that any nonnegative integer can be written as a sum of binomial coefficients with some prescribed properties. [less ▲]Detailed reference viewed: 23 (1 ULg)     1 2 3 4 5