Parikh Images of Register Automata

Authors Sławomir Lasota , Mohnish Pattathurajan

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Author Details

Sławomir Lasota
  • University of Warsaw, Poland
Mohnish Pattathurajan
  • University of Warsaw, Poland


We are grateful to Piotrek Hofman and Arka Ghosh for fruitful discussions.

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Sławomir Lasota and Mohnish Pattathurajan. Parikh Images of Register Automata. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Sets with atoms
  • register automata
  • Parikh images
  • rational sets
  • hierarchical register automata


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