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Let E be a regular expression. Our aim is to establish a theoretical relation between two well-known automata recognizing the language of E, namely the position automaton P E constructed by Glushkov or McNaughton and Yamada, and the equation automaton E E constructed by Mirkin or Antimirov. We define the notion of c-derivative (for canonical derivative) of(More)
Glushkov algorithm computes a nondeterministic nite automaton without-transition and with n + 1 states from a simple regular expression having n occurrences of letters. The aim of this paper is to give a set of necessary and suucient conditions characterizing this automaton. Our characterization theorem is formulated in terms of directed graphs. Moreover(More)
A nite-state machine is called a Thompson machine if it can be constructed from a regular expression using Thompson's construction. We call the underlying digraph of a Thompson machine a Thompson digraph. We characterize Thompson digraphs and, as one application of the characterization, we give an algorithm that generates an equivalent regular expression(More)
Le but de cet article est de présenter un nouvel algorithme séquentiel en temps Ω(n 2) pour la conversion d'une expression rationnelle simple, ayant n occurrences de symboles, en son automate de Glushkov (automate d'´ etats finis, non nécessairement déterministe, sans ε-transitions, ayant n + 1 ´ etats, représenté par sa table de transitions). Les(More)