References of "Rampersad, Narad"      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 1 to 10 of 10 1 Critical exponents of infinite balanced wordsRampersad, Narad; Shallit, Jeffrey; Vandomme, Elise in Theoretical Computer Science (2018), In pressOver an alphabet of size 3 we construct an infinite balanced word with critical exponent 2+\sqr{2}/2 . Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5+\sqr{5 ... [more ▼]Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2+\sqr{2}/2 . Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5+\sqr{5})/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated theorem prover Walnut. [less ▲]Detailed reference viewed: 12 (5 ULiège) The Formal Inverse of the Period-Doubling SequenceRampersad, Narad; Stipulanti, Manon in Journal of Integer Sequences (2018), 21(9), 189122If $p$ is a prime number, consider a p-automatic sequence $(u_n)_{n\ge 0}$, and let $U(X) =$\sum_{n\ge 0} u_nX^n ∈ F_p[[X]]$be its generating function. Assume that there exists a formal power series$V ... [more ▼]If $p$ is a prime number, consider a p-automatic sequence $(u_n)_{n\ge 0}$, and let $U(X) =$\sum_{n\ge 0} u_nX^n ∈ F_p[[X]]$be its generating function. Assume that there exists a formal power series$V(X) = \sum_{n\ge 0} v_n X^n ∈ F_p[[X]]$which is the compositional inverse of$U$, i.e.,$U(V(X)) = X = V(U(X))$. The problem investigated in this paper is to study the properties of the sequence$(v_n)_{n\ge 0}$. The work was first initiated for the Thue–Morse sequence, and more recently the case of other sequences (variations of the Baum-Sweet sequence, variations of the Rudin-Shapiro sequence and generalized Thue-Morse sequences) has been treated. In this paper, we deal with the case of the period-doubling sequence. We first show that the sequence of indices at which the period-doubling sequence takes the value 0 (resp., 1) is not k-regular for any$k \ge 2$. Secondly, we give recurrence relations for its formal inverse, then we show that it is 2-automatic, and we also provide an automaton that generates it. Thirdly, we study the sequence of indices at which this formal inverse takes the value 1, and we show that it is not k-regular for any$k \ge 2$by connecting it to the characteristic sequence of Fibonacci numbers. We leave as an open problem the case of the sequence of indices at which this formal inverse takes the value 0. [less ▲]Detailed reference viewed: 34 (1 ULiège) On the number of abelian bordered words (with an example of automatic theorem-proving)Goc, Daniel; Rampersad, Narad; Rigo, Michel et alin International Journal of Foundations of Computer Science (2014), 8In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible ... [more ▼]In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in$\mathbb{Z}$not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number of these words. In particular, over a$3$-letter alphabet, the connection with paths in the triangular lattice is made. Finally, we characterize the lengths of the abelian unbordered factors occurring in the Thue--Morse word using some kind of automatic theorem-proving provided by a logical characterization of the$k\$-automatic sequences. [less ▲]Detailed reference viewed: 29 (3 ULiège) A note on abelian returns in rotation wordsRampersad, Narad; Rigo, Michel ; Salimov, Pavel in Theoretical Computer Science (2014), 528Pursuing the study started by Rigo, Salimov and Vandomme, we use elementary number-theoretic techniques to characterize rotation words having a finite set of abelian returns to all prefixes. We also make ... [more ▼]Pursuing the study started by Rigo, Salimov and Vandomme, we use elementary number-theoretic techniques to characterize rotation words having a finite set of abelian returns to all prefixes. We also make the connection between the three gap theorem and the number of semi-abelian returns for Sturmian words, simplifying some arguments developed by Puzynina and Zamboni. [less ▲]Detailed reference viewed: 147 (19 ULiège) On the Number of Abelian Bordered WordsRampersad, Narad; Rigo, Michel ; Salimov, Pavel in Lecture Notes in Computer Science (2013), 7907In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible ... [more ▼]In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in Z not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number of these words. In particular, over a 3-letter alphabet, the connection with paths in the triangular lattice is made. Finally, we study the lengths of the abelian unbordered factors occurring in the Thue--Morse word. [less ▲]Detailed reference viewed: 97 (14 ULiège) Enumeration and decidable properties of automatic sequencesCharlier, Emilie ; Rampersad, Narad; Shallit, Jeffreyin International Journal of Foundations of Computer Science (2012), 23(5), 1035-1066We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related ... [more ▼]We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems. [less ▲]Detailed reference viewed: 39 (12 ULiège) Syntactic complexity of ultimately periodic sets of integers and application to a decision procedureLacroix, Anne ; Rampersad, Narad; Rigo, Michel et alin Fundamenta Informaticae (2012), 116We compute the cardinality of the syntactic monoid of the language 0* rep_b(mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any ... [more ▼]We compute the cardinality of the syntactic monoid of the language 0* rep_b(mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to a well studied problem: decide whether or not a b-recognizable set of integers is ultimately periodic. [less ▲]Detailed reference viewed: 110 (19 ULiège) Enumeration and decidable properties of automatic sequencesCharlier, Emilie ; Rampersad, Narad; Shallit, Jeffreyin Actes de Numération 2011 (2011, June)We show that various aspects of k-automatic sequences such as having an unbordered factor of length n are both decidable and e ectively enumerable. As a consequence it follows that many related sequences ... [more ▼]We show that various aspects of k-automatic sequences such as having an unbordered factor of length n are both decidable and e ectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give a new characterization of the class of k-regular sequences. Many results extend to other sequences de ned in terms of Pisot numeration systems. [less ▲]Detailed reference viewed: 26 (5 ULiège) The growth function of S-recognizable setsCharlier, Emilie ; Rampersad, Naradin Theoretical Computer Science (2011), 412(39), 5400-5408A set X ⊆ N is S-recognizable for an abstract numeration system S, if the set rep_S (X) of its representations is accepted by a finite automaton. We show that the growth function of an S-recognizable set ... [more ▼]A set X ⊆ N is S-recognizable for an abstract numeration system S, if the set rep_S (X) of its representations is accepted by a finite automaton. We show that the growth function of an S-recognizable set is always either Θ((log(n))^(c−df) n^f ) where c, d ∈ N and f ≥ 1, or Θ(n^r θ^(Θ(n^q))), where r, q ∈ Q with q ≤ 1. If the number of words of length n in the numeration language is bounded by a polynomial, then the growth function of an S-recognizable set is Θ(nr ), where r ∈ Q with r ≥ 1. Furthermore, for every r ∈ Q with r ≥ 1, we can provide an abstract numeration system S built on a polynomial language and an S-recognizable set such that the growth function of X is Θ(n^r ). For all positive integers k and ℓ, we can also provide an abstract numeration system S built on an exponential language and an S-recognizable set such that the growth function of X is Θ((log(n))^k n^ℓ). [less ▲]Detailed reference viewed: 26 (7 ULiège) Enumeration and decidable properties of automatic sequencesCharlier, Emilie ; Rampersad, Narad; Shallit, Jeffreyin Lecture Notes in Computer Science (2011), 6795We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related ... [more ▼]We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give a new characterization of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems. [less ▲]Detailed reference viewed: 23 (6 ULiège) 1