How Expressions Can Code for Automata

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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. If an automaton is then sufficiently “decorated”, the combination of these two algorithms gives the desired result. Reducing the amount of “decoration” is still the object of ongoing investigation.