Une extension d'un théorème de P. Jullien sur les âges de mots
Nous généralisons le théorème de Cobham ([2]), en démontrant qu'une partie infinie de ℕ est reconnaissable en base k (k entier strictement plus grand que un) et reconnaissable dans un système de numération associé à un nombre de Pisot unitaire (ayant une propriété arithmétique supplémentaire) si et seulement si elle est ultimement périodique.
Duplication is the replacement of a factor w within a word by ww. This operation can be used iteratively to generate languages starting from words or sets of words. By undoing duplications, one can eventually reach a square-free word, the original word's duplication root. The duplication root is unique, if the length of duplications is fixed. Based on these unique roots we define the concept of duplication code. Elementary properties are stated, then the conditions under which infinite duplication...
Sets of integers form a monoid, where the product of two sets A and B is defined as the set containing a+b for all and . We give a characterization of when a family of finite sets is a code in this monoid, that is when the sets do not satisfy any nontrivial relation. We also extend this result for some infinite sets, including all infinite rational sets.
Sets of integers form a monoid, where the product of two sets A and B is defined as the set containing a+b for all and . We give a characterization of when a family of finite sets is a code in this monoid, that is when the sets do not satisfy any nontrivial relation. We also extend this result for some infinite sets, including all infinite rational sets.
Cet article met l'accent sur l'originalité de la démarche adoptée. Dans le domaine de l'étude des sports collectifs, avec comme exemple de référence le rugby à XV, on se place du point de vue formel en utilisant des outils issus de l'informatique théorique. Les techniques de spécification mises en oeuvre sont les automates qui proviennent de la théorie des graphes, et la notation classique BNF, combinée aux Expressions Régulières, vue comme un langage de spécification formelle. L'un des intérêts...
We describe Wadge degrees of -languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is where is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].
We describe Wadge degrees of ω-languages recognizable by deterministic Turing machines. In particular, it is shown that the ordinal corresponding to these degrees is ξω where ξ = ω1CK is the first non-recursive ordinal known as the Church–Kleene ordinal. This answers a question raised in [2].
A multi-head 1-way pushdown automaton with heads is a pushdown automaton with 1-way read heads on the input tape and a stack. It was previously shown that the deterministic variant of the model cannot accept all the context free languages. In this paper, we introduce a 2-tape, 2-head model namely Watson-Crick pushdown automata where the content of the second tape is determined using a complementarity relation, similar to Watson-Crick automata. We show computational powers of nondeterministic...
We exhibit a new class of grammars with the help of weightfunctions. They are characterized by decreasing the weight during the derivation process. A decision algorithm for the emptiness problem is developed. This class contains non-contextfree grammars. The corresponding language class is identical to the class of ultralinear languages.