Document Open Access Logo

Probabilistic Regular Expressions and MSO Logic on Finite Trees

Author Thomas Weidner

PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2015.503.pdf
  • Filesize: 0.53 MB
  • 14 pages

Document Identifiers

Author Details

Thomas Weidner

Cite AsGet BibTex

Thomas Weidner. Probabilistic Regular Expressions and MSO Logic on Finite Trees. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 503-516, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.FSTTCS.2015.503

Abstract

We introduce probabilistic regular tree expressions and give a Kleene-like theorem for probabilistic tree automata (PTA). Furthermore, we define probabilistic MSO logic. This logic is more expressive than PTA. We define bottom-up PTA, which are strictly more expressive than PTA. Using bottom-up PTA, we prove a Büchi-like theorem for probabilistic MSO logic. We obtain a Nivat-style theorem as an additional result.
Keywords
  • Probabilistic Regular Expressions
  • MSO Logic
  • Tree Automata

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Parvaneh Babari and Manfred Droste. A Nivat theorem for weighted picture automata and weighted MSO logic. In Proc. of LATA 2015, volume 8977 of LNCS, pages 703-715. Springer, 2015. Google Scholar
  2. Mikołaj Bojańczyk. Forest expressions. In Computer Science Logic, volume 4646 of LNCS, pages 146-160. Springer, 2007. Google Scholar
  3. Mikołaj Bojańczyk, Mathias Samuelides, Thomas Schwentick, and Luc Segoufin. Expressive power of pebble automata. In ICALP 2006, volume 4051 of LNCS, pages 157-168. Springer, 2006. Google Scholar
  4. Benedikt Bollig, Paul Gastin, Benjamin Monmege, and Marc Zeitoun. A probabilistic Kleene theorem. In Proc. of ATVA 2012, volume 7561 of LNCS, pages 400-415. Springer, 2012. Google Scholar
  5. Arnaud Carayol, Axel Haddad, and Olivier Serre. Randomization in automata on infinite trees. ACM Trans. Comput. Log., 15(3):24, 2014. Google Scholar
  6. H. Comon, M. Dauchet, R. Gilleron, C. Löding, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree automata techniques and applications. Available on: http://www.grappa.univ-lille3.fr/tata, 2008. release November 18, 2008.
  7. Manfred Droste, Christian Pech, and Heiko Vogler. A Kleene theorem for weighted tree automata. Theory of Computing Systems, 38(1):1-38, 2005. Google Scholar
  8. Manfred Droste and Vitaly Perevoshchikov. A Nivat theorem for weighted timed automata and weighted relative distance logic. In Proc. of ICALP 2014, volume 8573 of LNCS, pages 171-182. Springer, 2014. Google Scholar
  9. Manfred Droste and Heiko Vogler. Weighted tree automata and weighted logics. Theoretical Computer Science, 366(3):228 - 247, 2006. Automata and Formal Languages. Google Scholar
  10. Manfred Droste and Heiko Vogler. Weighted logics for unranked tree automata. Theory Comput. Syst., 48(1):23-47, 2011. Google Scholar
  11. Clarence A. Ellis. Probabilistic tree automata. Information and Control, 19(5):401 - 416, 1971. Google Scholar
  12. Olympia Louscou-Bozapalidou. Stochastic tree functions. International Journal of Computer Mathematics, 52(3-4):149-160, 1994. Google Scholar
  13. M. Magidor and G. Moran. Probabilistic tree automata and context free languages. Israel Journal of Mathematics, 8(4):340-348, 1970. Google Scholar
  14. Benjamin Monmege. Specification and verification of quantitative properties: expressions, logics, and automata. PhD thesis, ENS Cachan, 2013. Google Scholar
  15. Frank Neven and Thomas Schwentick. Query automata over finite trees. Theor. Comput. Sci., 275(1-2):633-674, 2002. Google Scholar
  16. Maurice Nivat. Transductions des langages de Chomsky. Annales de l'institut Fourier, 18(1):339-455, 1968. Google Scholar
  17. Thomas Weidner. Probabilistic automata and probabilistic logic. In Proc. of MFCS 2012, volume 7464 of LNCS, pages 813-824. Springer, 2012. Google Scholar
  18. Thomas Weidner. Probabilistic ω-regular expressions. In Proc. of LATA 2014, volume 8370 of LNCS, pages 588-600. Springer, 2014. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact