As it has been recently shown, Parikh images of languages of nondeterministic one-register automata are rational (but not semilinear in general), but it is still open if the property extends to all register automata. We identify a subclass of nondeterministic register automata, called hierarchical register automata (HRA), with the following two properties: every rational language is recognised by a HRA; and Parikh image of the language of every HRA is rational. In consequence, these two properties make HRA an automata-theoretic characterisation of languages of nondeterministic register automata with rational Parikh images.
@InProceedings{lasota_et_al:LIPIcs.FSTTCS.2021.50, author = {Lasota, S{\l}awomir and Pattathurajan, Mohnish}, title = {{Parikh Images of Register Automata}}, booktitle = {41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)}, pages = {50:1--50:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-215-0}, ISSN = {1868-8969}, year = {2021}, volume = {213}, editor = {Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.50}, URN = {urn:nbn:de:0030-drops-155613}, doi = {10.4230/LIPIcs.FSTTCS.2021.50}, annote = {Keywords: Sets with atoms, register automata, Parikh images, rational sets, hierarchical register automata} }
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