Geodesic
On the solution of automaton equations
Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 104-116

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We consider the problem of solving automata equations in one variable. We suggest an algorithm for determining whether a given equation has a solution. We introduce the notion of a boundedly non-determinate function. It is proved that if an automaton equation has a solution, then the set of all solutions of this equation is embedded into some boundedly non-determinate function which can be effectively constructed on the base of the initial equation. 
@article{DM_2004_16_2_a7,
     author = {I. V. Lyalin},
     title = {On the solution of automaton equations},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2004_16_2_a7/}
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I. V. Lyalin. On the solution of automaton equations. Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 104-116. http://geodesic.mathdoc.fr/item/DM_2004_16_2_a7/