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Nondeterministic Tree-Walking Automata Are Not Closed Under Complementation

Authors Olga Martynova , Alexander Okhotin

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LIPIcs.ICALP.2025.168.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Models of computation
Keywords
  • Finite automata
  • tree-walking automata
  • complementation

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Abstract

It is proved that the family of tree languages recognized by nondeterministic tree-walking automata is not closed under complementation, solving a problem raised by Bojańczyk and Colcombet (https://doi.org/10.1137/050645427, SIAM J. Comp. 38 (2008) 658-701). In addition, it is shown that nondeterministic tree-walking automata are stronger than unambiguous tree-walking automata.

Cite As Get BibTex

Olga Martynova and Alexander Okhotin. Nondeterministic Tree-Walking Automata Are Not Closed Under Complementation. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 168:1-168:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.168

Author Details

Olga Martynova
  • Department of Mathematics and Computer Science, St. Petersburg State University, Russia
Alexander Okhotin
  • Department of Mathematics and Computer Science, St. Petersburg State University, Russia

Funding

Research supported by the Russian Science Foundation, project 23-11-00133.

References

  1. Alfred V. Aho and Jeffrey D. Ullman. Translations on a context-free grammar. Inf. Control., 19(5):439-475, 1971. URL: https://doi.org/10.1016/S0019-9958(71)90706-6.
  2. Mikołaj Bojańczyk. Tree-walking automata. In Carlos Martín-Vide, Friedrich Otto, and Henning Fernau, editors, Language and Automata Theory and Applications, Second International Conference, LATA 2008, Tarragona, Spain, March 13-19, 2008. Revised Papers, volume 5196 of Lecture Notes in Computer Science, pages 1-2. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-88282-4_1.
  3. Mikołaj Bojańczyk. It is undecidable if two regular tree languages can be separated by a deterministic tree-walking automaton. Fundam. Informaticae, 154(1-4):37-46, 2017. URL: https://doi.org/10.3233/FI-2017-1551.
  4. Mikołaj Bojańczyk and Thomas Colcombet. Tree-walking automata cannot be determinized. Theor. Comput. Sci., 350(2-3):164-173, 2006. URL: https://doi.org/10.1016/j.tcs.2005.10.031.
  5. Mikołaj Bojańczyk and Thomas Colcombet. Tree-walking automata do not recognize all regular languages. SIAM J. Comput., 38(2):658-701, 2008. URL: https://doi.org/10.1137/050645427.
  6. Mikołaj Bojańczyk, Mathias Samuelides, Thomas Schwentick, and Luc Segoufin. Expressive power of pebble automata. In Michele Bugliesi, Bart Preneel, Vladimiro Sassone, and Ingo Wegener, editors, Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Venice, Italy, July 10-14, 2006, Proceedings, Part I, volume 4051 of Lecture Notes in Computer Science, pages 157-168. Springer, 2006. URL: https://doi.org/10.1007/11786986_15.
  7. Thomas Colcombet. Unambiguity in automata theory. In Jeffrey O. Shallit and Alexander Okhotin, editors, Descriptional Complexity of Formal Systems - 17th International Workshop, DCFS 2015, Waterloo, ON, Canada, June 25-27, 2015. Proceedings, volume 9118 of Lecture Notes in Computer Science, pages 3-18. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-19225-3_1.
  8. Joost Engelfriet and Hendrik Jan Hoogeboom. Tree-walking pebble automata. In Juhani Karhumäki, Hermann A. Maurer, Gheorghe Păun, and Grzegorz Rozenberg, editors, Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa, pages 72-83. Springer, 1999. URL: https://doi.org/10.1007/978-3-642-60207-8_7.
  9. Joost Engelfriet and Hendrik Jan Hoogeboom. Automata with nested pebbles capture first-order logic with transitive closure. Log. Methods Comput. Sci., 3(2), 2007. URL: https://doi.org/10.2168/LMCS-3(2:3)2007.
  10. Mika Göös, Stefan Kiefer, and Weiqiang Yuan. Lower bounds for unambiguous automata via communication complexity. In Mikołaj Bojańczyk, Emanuela Merelli, and David P. Woodruff, editors, 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, July 4-8, 2022, Paris, France, volume 229 of LIPIcs, pages 126:1-126:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.ICALP.2022.126.
  11. Emil Indzhev and Stefan Kiefer. On complementing unambiguous automata and graphs with many cliques and cocliques. Inf. Process. Lett., 177:106270, 2022. URL: https://doi.org/10.1016/J.IPL.2022.106270.
  12. Michal Kunc and Alexander Okhotin. Reversibility of computations in graph-walking automata. Inf. Comput., 275:104631, 2020. URL: https://doi.org/10.1016/j.ic.2020.104631.
  13. Olga Martynova. Complexity of the emptiness problem for graph-walking automata and for tilings with star subgraphs. Inf. Comput., 296:105127, 2024. URL: https://doi.org/10.1016/J.IC.2023.105127.
  14. Anca Muscholl, Mathias Samuelides, and Luc Segoufin. Complementing deterministic tree-walking automata. Inf. Process. Lett., 99(1):33-39, 2006. URL: https://doi.org/10.1016/j.ipl.2005.09.017.
  15. Frank Neven. Automata, logic, and XML. In Julian C. Bradfield, editor, Computer Science Logic, 16th International Workshop, CSL 2002, 11th Annual Conference of the EACSL, Edinburgh, Scotland, UK, September 22-25, 2002, Proceedings, volume 2471 of Lecture Notes in Computer Science, pages 2-26. Springer, 2002. URL: https://doi.org/10.1007/3-540-45793-3_2.
  16. Frank Neven and Thomas Schwentick. On the power of tree-walking automata. Inf. Comput., 183(1):86-103, 2003. URL: https://doi.org/10.1016/S0890-5401(03)00013-0.
  17. Mathias Samuelides and Luc Segoufin. Complexity of pebble tree-walking automata. In Erzsébet Csuhaj-Varjú and Zoltán Ésik, editors, Fundamentals of Computation Theory, 16th International Symposium, FCT 2007, Budapest, Hungary, August 27-30, 2007, Proceedings, volume 4639 of Lecture Notes in Computer Science, pages 458-469. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74240-1_40.
  18. Michael Sipser. Halting space-bounded computations. Theor. Comput. Sci., 10:335-338, 1980. URL: https://doi.org/10.1016/0304-3975(80)90053-5.
  19. Margus Veanes. On computational complexity of basic decision problems of finite tree automata. UPMAIL Technical Report 133, Computing Science Department, Uppsala University, January 1997. Google Scholar
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