Skip to main content
SpringerLink
Log in

Weighted Unranked Tree Automata over Tree Valuation Monoids and Their Characterization by Weighted Logics

  • Conference paper
  • First Online:
Algebraic Informatics (CAI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9270))

Included in the following conference series:

Abstract

We introduce a new behavior of weighted unranked tree automata. We prove a characterization of this behavior by two fragments of weighted MSO logic and thereby provide a solution of an open equivalence problem of Droste and Vogler. The characterization works for valuation monoids as weight structures; they include all semirings and, in addition, enable us to cope with average.

D. Heusel—Partially supported by DFG Graduiertenkolleg 1763 (QuantLA).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bollig, B., Gastin, P.: Weighted versus probabilistic logics. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 18–38. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Brüggemann-Klein, A., Murata, M., Wood, D.: Regular tree and regular hedge languages over unranked alphabets: version 1. Technical Report HKUST-TCSC-2001-0, The Honkong University of Sience and Technologie (2001)

    Google Scholar 

  3. Brüggemann-Klein, A., Wood, D.: Regular tree languages over non-ranked alphabets (1998). http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.5397

  4. Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 385–400. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Chatterjee, K., Doyen, L., Henzinger, T.A.: Alternating weighted automata. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds.) FCT 2009. LNCS, vol. 5699, pp. 3–13. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Chatterjee, K., Doyen, L., Henzinger, T.A.: Probabilistic weighted automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 244–258. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Chatterjee, K., Doyen, L., Henzinger, T.A.: Expressiveness and closure properties for quantitative languages. In: Proceedings of LICS 2009, pp. 199–208. IEEE Computer Society (2009)

    Google Scholar 

  8. Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007). http://www.grappa.univ-lille3.fr/tata

  9. Droste, M., Gastin, P.: Weighted automata and weighted logics. Theoretical Computer Science 380, 69–86 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Droste, M., Götze, D., Märcker, S., Meinecke, I.: Weighted tree automata over valuation monoids and their characterization by weighted logics. In: Kuich, W., Rahonis, G. (eds.) Algebraic Foundations in Computer Science. LNCS, vol. 7020, pp. 30–55. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. EATCS Monographs on Theoretical Computer Science, Springer (2009)

    Google Scholar 

  12. Droste, M., Meinecke, I.: Weighted automata and weighted MSO logics for average- and longtime-behaviors. Information and Computation 220–221, 44–59 (2012)

    Article  MathSciNet  Google Scholar 

  13. Droste, M., Rahonis, G.: Weighted automata and weighted logics with discounting. Theory of Computing Systems 410(37), 3481–3494 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Droste, M., Vogler, H.: Weighted tree automata and weighted logics. Theoretical Computer Science 366, 228–247 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Droste, M., Vogler, H.: Weighted logics for unranked tree automata. Theory of Computing Systems 48, 23–47 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Droste, M., Vogler, H.: Kleene and Büchi theorems for weighted automata and multi-valued logics over arbitrary bounded lattices. Theoretical Computer Science 418, 14–36 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  17. Fichtner, I.: Weighted picture automata and weighted logics. Theory of Computing Systems 48(1), 48–78 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  18. Fülöp, Z., Vogler, H.: Weighted tree automata and tree transducers, chap. 9. In: Droste et al. [11] (2009)

    Google Scholar 

  19. Fülöp, Z., Vogler, H.: Forward and backward application of symbolic tree transducers. Acta Informatica 51, 297–325 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  20. Grätzer, G.: General Lattice Theory, 2nd edn. Birkhäuser Verlag (January 2003)

    Google Scholar 

  21. Högberg, J., Maletti, A., Vogler, H.: Bisimulation minimisation of weighted automata on unranked trees. Fundamenta Informaticae 92, 103–130 (2009)

    MATH  MathSciNet  Google Scholar 

  22. Libkin, L.: Logics for unranked trees: an overview. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 35–50. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Mathissen, C.: Definable transductions and weighted logics for texts. Theoretical Computer Science 411, 631–659 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  24. Mathissen, C.: Weighted logics for nested words and algebraic formal power series. Logical Methods in Computer Science 6 (2010)

    Google Scholar 

  25. Meinecke, I.: Weighted logics for traces. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 235–246. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  26. Murata, M.: Forest-regular languages and tree-regular languages (1995). (unpublished manuscript)

    Google Scholar 

  27. Neven, F.: Automata, logic, and XML. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, p. 2. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  28. Rahonis, G.: Weighted Muller tree automata and weighted logics. Journal of Automata, Languages and Combinatorics 12, 455–483 (2007)

    MATH  MathSciNet  Google Scholar 

  29. Tan, T.: Extending two-variable logic on data trees with order on data values and its automata. ACM Transactions on Computational Logic 15, 8:1–8:39 (2014)

    Article  Google Scholar 

  30. Thatcher, J.W.: Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. Journal of Computer and System Sciences 1, 317–322 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  31. Thomas, W.: Languages, automata, and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. A, pp. 389–455. Springer (1997)

    Google Scholar 

  32. Veanes, M., Bjørner, N.: Symbolic tree transducers. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol. 7162, pp. 377–393. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, D-04109, Leipzig, Germany

    Manfred Droste & Doreen Heusel

  2. Institut für Theoretische Informatik, Technische Universität Dresden, D-01062, Dresden, Germany

    Heiko Vogler

Authors
  1. Manfred Droste
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Doreen Heusel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Heiko Vogler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Heiko Vogler .

Editor information

Editors and Affiliations

  1. Institut für Maschinelle, Universität Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Andreas Maletti

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Droste, M., Heusel, D., Vogler, H. (2015). Weighted Unranked Tree Automata over Tree Valuation Monoids and Their Characterization by Weighted Logics. In: Maletti, A. (eds) Algebraic Informatics. CAI 2015. Lecture Notes in Computer Science(), vol 9270. Springer, Cham. https://doi.org/10.1007/978-3-319-23021-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23021-4_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23020-7

  • Online ISBN: 978-3-319-23021-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation