Directed Acyclic Subsequence Graph for multiple textsMaxime

The subsequence matching problem is to decide, for given strings S and T , whether S is a subsequence of T. The string S is called pattern and the string T text. We consider the case of multiple texts and show how to solve the subsequence matching problem in time linear in the length of pattern. For this purpose we build the automaton that accepts all subsequences of given texts. The automaton is called Directed Acyclic Subsequence Graph (DASG) and we present an algorithm for its building. We also prove upper bound for its number of states. Further, we consider modiication of the subsequence matching problem: given a string S and a nite language L, we are to decide whether S is a subsequence of any string in L. We suppose that a nite automaton accepting L is given and present an algorithm for building the DASG for the language L. We also mention applications of DASG to some problems related to subsequences. Le probl eme de recherche de sous-s equence consiste a d ecider, pour deux mots S et T , si S un sous-mot (sous-suite) de T. Le mot S est appel e le motif et le mot T le texte. Nous consid erons le cas de plusieurs textes et montrons comment r esoudre la question en temps lin eaire en la longueur du motif. Dans ce but, on construit un automate qui reconnait tous les sous-mots des textes. L'automate est appel e un DASG et on donne un algorithme pour le construire. Nous g en eralisons ensuite le probl eme a la recherche d'un motif dans un mot d'un langage rationnel L donn e par un automate. Finalement, nous mentionnons quelques applications de ces questions. This work has been done during the stay of Zden ek Tron cek at Institute Gaspard-Monge.