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Article Dans Une Revue RAIRO - Theoretical Informatics and Applications (RAIRO: ITA) Année : 2022

On rationally controlled one-rule insertion systems

Résumé

Rationally controlled one-rule insertion systems are one-rule string rewriting systems for which the rule, that is to insert a given word, may be applied in a word only behind a prefix that must belong to a given rational language called the control language. As for general string rewriting systems, these controlled insertion systems induce a transformation over languages: from a starting word, one can associate all its descendants. In this paper, we investigate the behavior of these systems in terms of preserving the classes of languages: finite, rational and context-free languages. We show that, even for very simple such systems, the images of finite or rational languages need not be context-free. In the case when the control language is in the form u* for some word u, we characterize one-rule insertion systems that induce a rational transduction and we prove that for these systems, the image of any context-free language is always context-free.
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Dates et versions

hal-03815815 , version 1 (14-10-2022)

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Michel Latteux, Yves Roos. On rationally controlled one-rule insertion systems. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2022, 56, pp.8. ⟨10.1051/ita/2022008⟩. ⟨hal-03815815⟩
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