Un cadre algébrique pour l'étude des monoïdes syntactiques
Deux remarques sur un théorème de S. Eilenberg
Automates finis
How expressions can code for automata
In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. We show here that if an automaton is then sufficiently “decorated”, the combination of these two algorithms...
How expressions can code for automata
In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. We show here that if an automaton is then sufficiently “decorated”, the combination of...
Corrigendum to our paper: How Expressions Can Code for Automata
In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an...
Radix enumeration of rational languages
We prove that the function that maps a word of a rational language onto its successor for the radix order in this language is a finite union of co-sequential functions.
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