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

Acknowledgements

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

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.FSTTCS.2021.50

Abstract

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
Keywords
  • Sets with atoms
  • register automata
  • Parikh images
  • rational sets
  • hierarchical register automata

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References

  1. Mikołaj Bojańczyk. Slightly infinite sets. A draft of a book. URL: https://www.mimuw.edu.pl/~bojan/paper/atom-book.
  2. Mikołaj Bojańczyk. Data monoids. In Proc. STACS 2011, volume 9 of LIPIcs, pages 105-116. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2011. Google Scholar
  3. Mikołaj Bojańczyk. Regular expressions for data words. Personal communication, 2020. Google Scholar
  4. Mikołaj Bojańczyk, Claire David, Anca Muscholl, Thomas Schwentick, and Luc Segoufin. Two-variable logic on data words. ACM Trans. Comput. Log., 12(4):27:1-27:26, 2011. Google Scholar
  5. Mikołaj Bojańczyk, Bartek Klin, and Slawomir Lasota. Automata with group actions. In Proc. LICS 2011, pages 355-364, 2011. Google Scholar
  6. Mikołaj Bojańczyk, Bartek Klin, and Slawomir Lasota. Automata theory in nominal sets. Log. Methods Comput. Sci., 10(3), 2014. Google Scholar
  7. Mikołaj Bojańczyk and Sławomir Lasota. An extension of data automata that captures XPath. Log. Methods Comput. Sci., 8(1), 2012. Google Scholar
  8. Mikołaj Bojańczyk and Rafał Stefański. Single-use automata and transducers for infinite alphabets. In Proc. ICALP 2020, volume 168 of LIPIcs, pages 113:1-113:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  9. Thomas Colcombet, Clemens Ley, and Gabriele Puppis. Logics with rigidly guarded data tests. Log. Methods Comput. Sci., 11(3), 2015. Google Scholar
  10. Thomas Colcombet and Amaldev Manuel. Generalized data automata and fixpoint logic. In Proc. FSTTCS 2014, volume 29 of LIPIcs, pages 267-278. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014. Google Scholar
  11. Loris D'Antoni and Margus Veanes. Minimization of symbolic automata. In Proc. POPL '14, pages 541-554. ACM, 2014. Google Scholar
  12. Stéphane Demri and Ranko Lazic. LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log., 10(3):16:1-16:30, 2009. Google Scholar
  13. Samuel Eilenberg. Automata, languages, and machines. A. Pure and applied mathematics. Academic Press, 1974. URL: https://www.worldcat.org/oclc/310535248.
  14. Nissim Francez and Michael Kaminski. Finite-memory automata. Theor. Comput. Sci., 134(2):329-363, 1994. Google Scholar
  15. Nissim Francez and Michael Kaminski. An algebraic characterization of deterministic regular languages over infinite alphabets. Theor. Comput. Sci., 306(1-3):155-175, 2003. Google Scholar
  16. Piotr Hofman, Marta Juzepczuk, Slawomir Lasota, and Mohnish Pattathurajan. Parikh’s theorem for infinite alphabets. In 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021, Rome, Italy, June 29 - July 2, 2021, pages 1-13. IEEE, 2021. Google Scholar
  17. Michael Kaminski and Tony Tan. Regular expressions for languages over infinite alphabets. Fundam. Informaticae, 69(3):301-318, 2006. Google Scholar
  18. Alexander Kurz, Tomoyuki Suzuki, and Emilio Tuosto. On nominal regular languages with binders. In Lars Birkedal, editor, Proc. FOSSACS 2012, volume 7213 of Lecture Notes in Computer Science, pages 255-269. Springer, 2012. Google Scholar
  19. Leonid Libkin, Tony Tan, and Domagoj Vrgoc. Regular expressions for data words. J. Comput. Syst. Sci., 81(7):1278-1297, 2015. Google Scholar
  20. Tova Milo, Dan Suciu, and Victor Vianu. Typechecking for XML transformers. J. Comput. Syst. Sci., 66(1):66-97, 2003. Google Scholar
  21. Frank Neven, Thomas Schwentick, and Victor Vianu. Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log., 5(3):403-435, 2004. Google Scholar
  22. A. M. Pitts. Nominal Sets: Names and Symmetry in Computer Science, volume 57 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 2013. Google Scholar
  23. Hiroshi Sakamoto and Daisuke Ikeda. Intractability of decision problems for finite-memory automata. Theor. Comput. Sci., 231(2):297-308, 2000. Google Scholar
  24. Luc Segoufin. Automata and logics for words and trees over an infinite alphabet. In Proc. CSL 2006, volume 4207 of Lecture Notes in Computer Science, pages 41-57. Springer, 2006. Google Scholar
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