References of "Charlier, Emilie"      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 66     1 2 3 4     S-automatic setsCharlier, Emilie Scientific conference (2010, December)In this talk, I will discuss some new properties of S-automatic sets. First I will show that a multidimensional set is S-automatic for all abstract numeration systems S if and only if it is 1-automatic ... [more ▼]In this talk, I will discuss some new properties of S-automatic sets. First I will show that a multidimensional set is S-automatic for all abstract numeration systems S if and only if it is 1-automatic. This result is surprising in the following sense: the class of multidimensional 1-automatic sets is a strict subclass of that of semi-linear sets. Hence, this result is not a generalization of the well-known result in integer base numeration systems: a multidimensional set is b-automatic for all integer bases b ≥ 1 if and only if it is semi-linear. Second I will describe the possible behaviors of the nth -term of an S-automatic set, depending on the growth function (i.e., the number of words of length n) of the numeration language. [less ▲]Detailed reference viewed: 31 (1 ULiège) Criteria for recognizability in abstract numeration systemsCharlier, Emilie Scientific conference (2010, October)In this talk, I will first shortly introduce abstract numeration systems. Then I will prove some first results I have regarding the growth function of recognizable sets. I will conjecture which functions ... [more ▼]In this talk, I will first shortly introduce abstract numeration systems. Then I will prove some first results I have regarding the growth function of recognizable sets. I will conjecture which functions can be the growth functions of recognizable sets in general, depending on the growth functions of the numeration language and of the sublanguage under consideration. [less ▲]Detailed reference viewed: 14 (0 ULiège) 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: 100 (19 ULiège) 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: 133 (20 ULiège) Representing real numbers in a generalized numeration systemCharlier, Emilie Conference (2010, June)We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers ... [more ▼]We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show that our framework can be applied to the rational base numeration systems. [less ▲]Detailed reference viewed: 11 (3 ULiège) 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: 69 (9 ULiège) 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: 82 (17 ULiège) Abstract Numeration Systems : Recognizability, Decidability, Multidimensional S-Automatic Words, and Real NumbersCharlier, Emilie Doctoral thesis (2009)In this dissertation we study and we solve several questions regarding abstract numeration systems. Each particular problem is the focus of a chapter. The first problem concerns the study of the ... [more ▼]In this dissertation we study and we solve several questions regarding abstract numeration systems. Each particular problem is the focus of a chapter. The first problem concerns the study of the preservation of recognizability under multiplication by a constant in abstract numeration systems built on polynomial regular languages. The second is a decidability problem, which has been already studied notably by J. Honkala and A. Muchnik and which is studied here for two new cases: the linear positional numeration systems and the abstract numeration systems. Next, we focus on the extension to the multidimensional setting of a result of A. Maes and M. Rigo regarding S-automatic infinite words. Finally, we propose a formalism to represent real numbers in the general framework of abstract numeration systems built on languages that are not necessarily regular. We end by a list of open questions in the continuation of the present work. [less ▲]Detailed reference viewed: 205 (46 ULiège) 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: 47 (16 ULiège) Multidimensional generalized automatic sequences and shape-symmetric morphic wordsCharlier, Emilie ; Kärki, Tomi; Rigo, Michel in Proceedings of AutoMathA (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 paper, we ... [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 paper, we consider an analogous definition in a multidimensional setting and study the relationship with the shape-symmetric infinite words as introduced by Arnaud Maes. Precisely, for d ≥ 2, we show that a multidimensional infinite word x : N^d → Σ over a finite alphabet Σ 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: 20 (3 ULiège) 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: 105 (31 ULiège) A decision problem for ultimately periodic sets in non-standard numeration systemsCharlier, Emilie Scientific conference (2008, December)Given a linear numeration system U and a set X (include in N) such that repU(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X is ultimately periodic, i.e., whether ... [more ▼]Given a linear numeration system U and a set X (include in N) such that repU(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X is ultimately periodic, i.e., whether or not X is a finite union of arithmetic progressions? Honkala showed that this problem turns out to be decidable for the usual b-ary numeration system (b greater than 2) defined by U_n = bU_{n-1} for n greater than 1 and U_0 = 1. In this work, we give a decision procedure for this problem for a large class of linear numeration systems. [less ▲]Detailed reference viewed: 17 (1 ULiège) A decision problem for ultimately periodic sets in non-standard numeration systemsCharlier, Emilie Conference (2008, May)We consider the following decidability problem: Given a linear numeration system U and a set X ⊆ N such that rep_U(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X ... [more ▼]We consider the following decidability problem: Given a linear numeration system U and a set X ⊆ N such that rep_U(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X is ultimately periodic, i.e., whether or not X is a finite union of arithmetic progressions? In this work, we give a decision procedure for this problem whenever U is a linear numeration system such that N is U -recognizable and satisfying a relation of the form U_{i+k} = a_1 U_{i+k−1} + · · · + a_k U_i with a_k = ±1 (the main reason for this assumption is that 1 and −1 are the only two integers invertible modulo n for all n ≥ 2). [less ▲]Detailed reference viewed: 22 (4 ULiège) Systèmes de numérationCharlier, Emilie Scientific conference (2008, February)Dans cet exposé, je propose une introduction aux systèmes de numération en général : bases entières, numérations linéaires, numérations abstraites. Je donnerai les premiers résultats et attirerai l ... [more ▼]Dans cet exposé, je propose une introduction aux systèmes de numération en général : bases entières, numérations linéaires, numérations abstraites. Je donnerai les premiers résultats et attirerai l'attention sur différents axes de recherche possibles. [less ▲]Detailed reference viewed: 10 (1 ULiège) 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: 42 (7 ULiège) 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: 25 (3 ULiège) 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: 30 (13 ULiège) Abstract numeration systemsCharlier, Emilie Conference (2007, May)In this talk, I will introduce abstract numeration systems in general and present some results I have regarding operation preserving regularity. In particular, I will focus on multiplication by a constant.Detailed reference viewed: 12 (1 ULiège) Structural properties of bounded languages with respect to multiplication by a constantCharlier, Emilie Conference (2007, April)Generalizations of positional number systems in which N is recognizable by finite automata are obtained by describing an arbitrary infinite regular language according to the genealogical ordering. More ... [more ▼]Generalizations of positional number systems in which N is recognizable by finite automata are obtained by describing an arbitrary infinite regular language according to the genealogical ordering. More precisely, an abstract numeration system is a triple S = (L, Σ, <) where L is an infinite language over the totally ordered alphabet (Σ, <). Enumerating the elements of L genealogically with respect to < leads to a one-to-one map rS from N onto L. To any natural number n, it assigns the (n + 1)th word of L, its S-representation, while the inverse map valS sends any word belonging to L onto its numerical value. A subset X is said to be S-recognizable if rS (X) is a regular subset of L. We study the preservation of recognizability of a set of integers after multiplication by a constant for abstract numeration systems built over a bounded language. [less ▲]Detailed reference viewed: 13 (4 ULiège) Abstract numeration systems and recognizabilityCharlier, Emilie Conference (2007, January)In this talk, I will present some results concerning multiplication by a constant in an abstract numeration system built on a bounded language. More precisely, we will show that this operation does not ... [more ▼]In this talk, I will present some results concerning multiplication by a constant in an abstract numeration system built on a bounded language. More precisely, we will show that this operation does not preserve regularity, and therefore cannot be computed by a finite automaton. [less ▲]Detailed reference viewed: 11 (1 ULiège)     1 2 3 4