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Investigations on Hotz groups for arbitrary grammars

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Summary

The Hotz group H(G) and the Hotz monoid M(G) of an arbitrary grammar G=(V, X, P, S) are defined by H(G)=F(V∪X)/P and M(G) =(V∪X)*/P respectively. A language L⊂X* is called a language with Hotz isomorphism if there exists a grammar G with L=L(G) such that the natural homomorphism F(X)/L→H(G) is an isomorphism. The main result of this paper states that homomorphic images of sentential form languages are languages with Hotz isomorphism. This is a generalization of a result of Frougny, Sakarovitch, and Valkema on context-free languages.

Hotz groups are used to obtain lower bounds for the number of productions which are needed to generate a language. Further it is shown that there are languages with Hotz isomorphism without being a homomorphic image of a sentential form language, and there are context-sensitive languages without Hotz isomorphism. The theory of Hotz monoids is used to get some results on languages generated by grammars with a symmetric set of rules.

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  1. Fachbereich Informatik, Rothenbaumchaussee 67-69, D-2000, Hamburg 13, Federal Republic of Germany

    Volker Diekert

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  1. Volker Diekert
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Diekert, V. Investigations on Hotz groups for arbitrary grammars. Acta Informatica 22, 679–698 (1986). https://doi.org/10.1007/BF00263651

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