242 research outputs found
Formal Properties of XML Grammars and Languages
XML documents are described by a document type definition (DTD). An
XML-grammar is a formal grammar that captures the syntactic features of a DTD.
We investigate properties of this family of grammars. We show that every
XML-language basically has a unique XML-grammar. We give two characterizations
of languages generated by XML-grammars, one is set-theoretic, the other is by a
kind of saturation property. We investigate decidability problems and prove
that some properties that are undecidable for general context-free languages
become decidable for XML-languages. We also characterize those XML-grammars
that generate regular XML-languages.Comment: 24 page
Coding rotations on intervals
We show that the coding of rotation by on intervals with
rationally independent lengths can be recoded over Sturmian words of angle
More precisely, for a given an universal automaton is constructed such
that the edge indexed by the vector of values of the th letter on each
Sturmian word gives the value of the th letter of the coding of rotation.Comment: LIAFA repor
Splicing systems and the Chomsky hierarchy
In this paper, we prove decidability properties and new results on the
position of the family of languages generated by (circular) splicing systems
within the Chomsky hierarchy. The two main results of the paper are the
following. First, we show that it is decidable, given a circular splicing
language and a regular language, whether they are equal. Second, we prove the
language generated by an alphabetic splicing system is context-free. Alphabetic
splicing systems are a generalization of simple and semi-simple splicin systems
already considered in the literature
Sur la construction de mots sans carré
http://www-igm.univ-mlv.fr/~berstel/Articles/1979SeminaireBordeaux.pdfSéminaire de Théorie des Nombres 1978-1979. Exp. No. 18On montre que les quatre constructions de Thue, Morse-Hedlund, Braunholtz et Istrail définissent le même mot infini sans carré. On étudie alors leur lien avec les tag-systèmes. Enfin, on prouve que l'ensembel des mots infinis sans carré sur un alphabet à trois lettres n'est pas dénombrable
Operations preserving recognizable languages
Given a strictly increasing sequence s of non-negative integers, filtering a word a_0a_1 ... a_n by s consists in deleting the letters ai such that i is not in the set {s_0, s_1, ...}. By a natural generalization, denote by L[s], where L is a language, the set of all words of L filtered by s. The filtering problem is to characterize the filters s such that, for every regular language L, L[s] is regular. In this paper, the filtering problem is solved, and a unified approach is provided to solve similar questions, including the removal problem considered by Seiferas and McNaughton. Our approach relies on a detailed study of various residual notions, notably residually ultimately periodic sequences and residually rational transductions
The complexity of tangent words
In a previous paper, we described the set of words that appear in the coding
of smooth (resp. analytic) curves at arbitrary small scale. The aim of this
paper is to compute the complexity of those languages.Comment: In Proceedings WORDS 2011, arXiv:1108.341
Recurrent Partial Words
Partial words are sequences over a finite alphabet that may contain wildcard
symbols, called holes, which match or are compatible with all letters; partial
words without holes are said to be full words (or simply words). Given an
infinite partial word w, the number of distinct full words over the alphabet
that are compatible with factors of w of length n, called subwords of w, refers
to a measure of complexity of infinite partial words so-called subword
complexity. This measure is of particular interest because we can construct
partial words with subword complexities not achievable by full words. In this
paper, we consider the notion of recurrence over infinite partial words, that
is, we study whether all of the finite subwords of a given infinite partial
word appear infinitely often, and we establish connections between subword
complexity and recurrence in this more general framework.Comment: In Proceedings WORDS 2011, arXiv:1108.341
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