Contributions à l'étude de la dérivation des expressions rationnelles et à l'étude des systèmes de numération abstraits

Abstract : The works in this thesis lies in the automata and formal languages theory. in the first part, the notion of derivation of rational expressions is studied. more precisely the broken derived terms of a rational expressions. Theses broken derived terms allow, under certain circumstances, with some other operations on automata, to have the reversibility of the transformation of an automaton into a rational expression. In the second part, automata and tranducers allow to 'count' on a numeration system, where integers are represented by words on a rational language. more precisely, this part adress the problem of counting in an abstract numeration systems, which maps to any word of a rational language, ordored by radix order, the integer corresponding to the order of the word. in such a numeration system, the function which computes the successor of a word is a piecewise co-sequential function: it can be realised by a machine which reads the input two times to give the output.
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Pierre-Yves Angrand. Contributions à l'étude de la dérivation des expressions rationnelles et à l'étude des systèmes de numération abstraits. Autre [cs.OH]. Télécom ParisTech, 2012. Français. ⟨NNT : 2012ENST0009⟩. ⟨pastel-00850633⟩

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