arXiv subjects
Publications and source records attributed to Luc Boasson.
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a relaxation of the condition used in the case of finite words. In the annex, we prove that the factorization of a rational word has a special form and that it can be computed from a rational expression describing the word.
A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing systems, introduced by Păun and subsequently developed by many researchers in both linear and circular case of splicing definition. In particular, we will present recent results on this topic and how they stimulate new challenging investigations.
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.
This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text processing, image analysis, linguistic computer science, and many other applications. There are two main families of minimization algorithms. The first by a sequence of refinements of a partition of the set of states, the second by a sequence of fusions or merges of states. Hopcroft's and Moore's algorithms belong to the first family, the linear-time minimization of acyclic automata of Revuz belongs to the second family. One of our studies is upon the comparison of the nature of Moore's and Hopcroft's algorithms. This gives some new insight in both algorithms. As we shall see, these algorithms are quite different both in behavior and in complexity. In particular, we show that it is not possible to simulate the computations of one of the algorithm by the other. We describe the minimization algorithm by fusion for so-called local automata. A special case of minimization is the construction o minimal automata for finite sets. We consider briefly this case, and in particular describe incremental algorithms. Finally, we consider the case of updating a minimal automaton when a word is added or removed from the set it recognizes.
We show that there exists an uniformly recurrent infinite word whose set of factors is closed under reversal and which has only finitely many palindromic factors.
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.