RAIRO-Theor. Inf. Appl.
Volume 56, 2022
|Number of page(s)||31|
|Published online||14 October 2022|
On rationally controlled one-rule insertion systems
CRIStAL, University of Lille, France
* Corresponding author: firstname.lastname@example.org
Accepted: 6 September 2022
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.
Mathematics Subject Classification: 68Q45 / 68Q42 / 68R15
Key words: String rewriting / context-free languages
© The authors. Published by EDP Sciences, 2022
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