How expressions can code for automata

Abstract:

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
[ND: rational = regular]
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 gives the desired result. Reducing the
amount of "decoration" is still the object of ongoing investigation.