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A new normal form for the compositions of morphisms and inverse morphisms. (English) Zbl 0638.68087
It is shown that for every composition $$\tau$$ of morphisms and inverse morphisms there exist morphisms $$h_ 1$$, $$h_ 2$$, $$h_ 3$$, and $$h_ 4$$ such that $$\tau =h_ 4^{-1}\circ h_ 3\circ h_ 2^{-1}\circ h_ 1$$. This solves a problem raised by the first author and J. Leguy [Lect. Notes Comput. Sci. 154, 420-432 (1983; Zbl 0523.68067)] and partially solved by the second author [Ann. Univ. Turku, Ser. A I 186, 118-128 (1984; Zbl 0541.68045)].

##### MSC:
 68Q45 Formal languages and automata
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##### References:
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