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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:

[1] J. Berstel,Transductions and Context-Free Languages, B. G. Teubner, Stuttgart, 1979. · Zbl 0424.68040
[2] K. Culik II, F. E. Fich, and A. Salomaa, A homomorphic characterization of regular languages,Discrete Appl. Math.,4 (1982), 149–152. · Zbl 0481.68069 · doi:10.1016/0166-218X(82)90072-5
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[5] M. Latteux and J. Leguy, On the composition of morphisms and inverse morphisms,Lecture Notes Comput. Sci.,154 (1983), 420–432. · Zbl 0523.68067 · doi:10.1007/BFb0036926
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