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 41 to 60 of 99     1 2 3 4 5     Arithmétique, Automates et Géométrie discrèteAllouche, Jean-Paul; Rigo, Michel Diverse speeche and writing (2011)cours au Collège BelgiqueDetailed reference viewed: 52 (9 ULg) State complexity of testing divisibilityCharlier, Emilie ; Rampersad, Narad ; Rigo, Michel et alin McQuillan, Ian, Pighizzini, Giovanni (Ed.) Proceedings Twelfth Annual Workshop on Descriptional Complexity of Formal Systems (2010, August)Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m>=2 for a wide class of linear numeration systems. As an ... [more ▼]Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m>=2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of mN in the Fibonacci system is exactly 2m^2. [less ▲]Detailed reference viewed: 71 (19 ULg) Structure of the minimal automaton of a numeration languageCharlier, Emilie ; Rampersad, Narad ; Rigo, Michel et alin Actes de LaCIM 2010 (2010, August)We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly ... [more ▼]We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show that for any automaton A arising from a system with a dominant root beta>1, there is a morphism mapping A onto the automaton arising from the Bertrand system associated with the number beta. [less ▲]Detailed reference viewed: 93 (20 ULg) Invariant gamesDuchêne, Eric; Rigo, Michel in Theoretical Computer Science (2010), 411In the context of 2-player removal games, we define the notion of invariant game for which each allowed move is independent of the position it is played from. We present a family of invariant games which ... [more ▼]In the context of 2-player removal games, we define the notion of invariant game for which each allowed move is independent of the position it is played from. We present a family of invariant games which are variations of Wythoff's game. The set of P-positions of these games are given by a pair of complementary Beatty sequences related to the irrational quadratic number $\alpha_k = (1; \overline{1, k})$. We also provide a recursive characterization of this set. [less ▲]Detailed reference viewed: 70 (30 ULg) Systèmes de numération abstraits et combinatoire des mots (habilitation à diriger des recherches)Rigo, Michel Post doctoral thesis (2010)We summary the main properties of abstract numeration systems and their links to combinatorics on words and combinatorial game theory.Detailed reference viewed: 117 (34 ULg) Extensions and restrictions of Wythoff's game preserving its P positionsDuchêne, Eric; Fraenkel, Aviezri; Nowakowski, Richard et alin Journal of Combinatorial Theory - Series A (2010), 117We consider extensions and restrictions of Wythoff's game having exactly the same set of P positions as the original game. No strict subset of rules give the same set of P positions. On the other hand, we ... [more ▼]We consider extensions and restrictions of Wythoff's game having exactly the same set of P positions as the original game. No strict subset of rules give the same set of P positions. On the other hand, we characterize all moves that can be adjoined while preserving the original set of P positions. Testing if a move belongs to such an extended set of rules is shown to be doable in polynomial time. Many arguments rely on the infinite Fibonacci word, automatic sequences and the corresponding number system. With these tools, we provide new two-dimensional morphisms generating an infinite picture encoding respectively P positions of Wythoff's game and moves that can be adjoined. [less ▲]Detailed reference viewed: 71 (16 ULg) Special issue dedicated to the twelfth "Journées montoises d'informatique théorique"Bruyère, Véronique; Rigo, Michel in RAIRO : Informatique Théorique et Applications = Theoretical Informatics and Applications (2010), 44(1), 1-192Detailed reference viewed: 16 (3 ULg) Special issue dedicated to the second "AutoMathA conference"Bruyère, Véronique; Pin, Jean-Eric; Restivo, Antonio et alin Discrete Mathematics & Theoretical Computer Science (2010), 12Detailed reference viewed: 10 (0 ULg) Structure of the minimal automaton of a numeration language and applications to state complexityCharlier, Emilie ; Rampersad, Narad ; Rigo, Michel et alin Actes des Journées Montoises d'Informatique Théorique (2010)We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly ... [more ▼]We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show that for any automaton A arising from a system with a dominant root > 1, there is a morphism mapping A onto the automaton arising from the Bertrand system associated with the number . Under some mild assumptions, we also study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m>=2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of mN in the Fibonacci system is exactly 2m^2. [less ▲]Detailed reference viewed: 44 (7 ULg) Multidimensional generalized automatic sequences and shape-symmetric morphic wordsCharlier, Emilie ; Kärki, Tomi; Rigo, Michel in Discrete Mathematics (2010), 310An infinite word is S-automatic if, for all n>=0, its (n+1)st letter is the output of a deterministic automaton fed with the representation of n in the numeration system S. In this paper, we consider an ... [more ▼]An infinite word is S-automatic if, for all n>=0, its (n+1)st letter is the output of a deterministic automaton fed with the representation of n in the numeration system S. In this paper, we consider an analogous definition in a multidimensional setting and study its relation to the shapesymmetric infinite words introduced by Arnaud Maes. More precisely, for d>1, we show that a multidimensional infinite word x over a finite alphabet is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word. [less ▲]Detailed reference viewed: 57 (16 ULg) On the Recognizability of Self-Generating SetsKärki, Tomi; Lacroix, Anne ; Rigo, Michel in Journal of Integer Sequences (2010), 13Let I be a finite set of integers and F be a finite set of maps of the form n->k_i n + l_i with integer coefficients. For an integer base k>=2, we study the k-recognizability of the minimal set X of ... [more ▼]Let I be a finite set of integers and F be a finite set of maps of the form n->k_i n + l_i with integer coefficients. For an integer base k>=2, we study the k-recognizability of the minimal set X of integers containing I and satisfying f(X)\subseteq X for all f in F. In particular, solving a conjecture of Allouche, Shallit and Skordev, we show under some technical conditions that if two of the constants k_i are multiplicatively independent, then X is not k-recognizable for any k>=2. [less ▲]Detailed reference viewed: 31 (9 ULg) Mathémagie et au-delàRigo, Michel Learning material (2010)Nous présentons ici 5 tours de magie ne nécessitant aucune habileté particulière de la part de l'apprenti magicien : des tours de cartes, des tours de divination et le célèbre tour du barman aveugle ... [more ▼]Nous présentons ici 5 tours de magie ne nécessitant aucune habileté particulière de la part de l'apprenti magicien : des tours de cartes, des tours de divination et le célèbre tour du barman aveugle avec des gants de boxe''. Contrairement au magicien qui ne dévoile jamais ses secrets, ici, nous expliquons que ces tours reposent sur diverses propriétés et constructions mathématiques. Ces dernières débouchent sur de véritables questions de recherche actuelle en théorie des graphes ou en combinatoire des mots et même sur de possibles applications en robotique et automatisation ! Il y en aura donc pour tous les goûts... et tous les niveaux (suivant l'auditoire, l'exposé sera adapté au niveau des élèves de la 4ième à la 6ième secondaire, voire même aux étudiants universitaires). Ce texte présente donc un matériel qui dépassera souvent (et de loin) le spectacle''. [less ▲]Detailed reference viewed: 308 (21 ULg) Index and ReferencesBerthé, Valérie; Rigo, Michel in Combinatorics, Automata and Number Theory (2010)Detailed reference viewed: 9 (1 ULg) Abstract numeration systems (Chapter 3)Lecomte, Pierre ; Rigo, Michel in Berthé, Valérie; Rigo, Michel (Eds.) Combinatorics, Automata and Number Theory (2010)Detailed reference viewed: 82 (9 ULg) Preliminaries (Chapter 1)Berthé, Valérie; Rigo, Michel in Berthé, Valérie; Rigo, Michel (Eds.) Combinatorics, Automata and Number Theory (2010)Detailed reference viewed: 10 (2 ULg) IntroductionBerthé, Valérie; Rigo, Michel in Rigo, Michel; Berthé, Valérie (Eds.) Combinatorics, Automata and Number Theory (2010)Detailed reference viewed: 9 (3 ULg) On the Periodicity of Morphic WordsHalava, Vesa; Harju, Tero; Kärki, Tomi et alin Lecture Notes in Computer Science (2010), 6224Given a morphism h prolongable on a and an integer p, we present an algorithm that calculates which letters occur infinitely often in congruent positions modulo p in the infinite word hω(a). As a ... [more ▼]Given a morphism h prolongable on a and an integer p, we present an algorithm that calculates which letters occur infinitely often in congruent positions modulo p in the infinite word hω(a). As a corollary, we show that it is decidable whether a morphic word is ultimately p-periodic. Moreover, using our algorithm we can find the smallest similarity relation such that the morphic word is ultimately relationally p-periodic. The problem of deciding whether an automatic sequence is ultimately weakly R-periodic is also shown to be decidable. [less ▲]Detailed reference viewed: 59 (12 ULg) Numeration Systems: a Link between Number Theory and Formal Language TheoryRigo, Michel in Lecture Notes in Computer Science (2010), 6224We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal ... [more ▼]We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions. We discuss the notion of numeration systems, recognizable sets of integers and automatic sequences. We brie y sketch some results about transcendence related to the representation of real numbers. We conclude with some applications to combinatorial game theory and veri cation of in nite-state systems and present a list of open problems. [less ▲]Detailed reference viewed: 83 (12 ULg) Invariant gamesDuchêne, Eric; Rigo, Michel Conference (2009, September)In the context of 2-player removal games, we define the notion of invariant game for which each allowed move is independent of the position it is played from. We present a family of invariant games which ... [more ▼]In the context of 2-player removal games, we define the notion of invariant game for which each allowed move is independent of the position it is played from. We present a family of invariant games which are variations of Wythoff's game. The set of P-positions of these games are given by a pair of complementary Beatty sequences related to the irrational quadratic number $\alpha_k = (1; \overline{1, k})$. We also provide a recursive characterization of this set. [less ▲]Detailed reference viewed: 34 (7 ULg) A characterization of multidimensional S-automatic sequencesCharlier, Emilie ; Kärki, Tomi ; Rigo, Michel in Actes des rencontres du CIRM, 1 (2009)An infinite word is S-automatic if, for all n ≥ 0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this extended ... [more ▼]An infinite word is S-automatic if, for all n ≥ 0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d ≥ 2, we state that a multidimensional infinite word x : N^d → \Sigma over a finite alphabet \Sigma is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word. [less ▲]Detailed reference viewed: 41 (14 ULg)     1 2 3 4 5