Skip to main content
SpringerLink
Log in

Pebble Weighted Automata and Transitive Closure Logics

  • Conference paper
Automata, Languages and Programming (ICALP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6199))

Included in the following conference series:

Abstract

We introduce new classes of weighted automata on words. Equipped with pebbles and a two-way mechanism, they go beyond the class of recognizable formal power series, but capture a weighted version of first-order logic with bounded transitive closure. In contrast to previous work, this logic allows for unrestricted use of universal quantification. Our main result states that pebble weighted automata, nested weighted automata, and this weighted logic are expressively equivalent. We also give new logical characterizations of the recognizable series.

Supported by fp7 Quasimodo, anr-06-seti-003 dots, arcus Île de France-Inde.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Berstel, J., Reutenauer, C.: Recognizable formal power series on trees. TCS 18(2), 115–148 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bojańczyk, M.: Tree-walking automata. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 1–17. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Bojańczyk, M., Samuelides, M., Schwentick, T., Segoufin, L.: Expressive power of pebble automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 157–168. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Bollig, B., Gastin, P., Monmege, B., Zeitoun, M.: Pebble weighted automata and transitive closure logics, http://www.lsv.ens-cachan.fr/Publis/RAPPORTS_LSV/rapports

  5. Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik Grundlagen Math. 6, 66–92 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  6. Droste, M., Gastin, P.: Weighted automata and weighted logics. Theoretical Computer Science 380(1-2), 69–86 (2007); Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.): ICALP 2005. LNCS, vol. 3580, pp. 513–525. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  7. Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. EATCS Monographs in Theoret. Comput. Sci. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  8. Elgot, C.C.: Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc. 98, 21–52 (1961)

    MathSciNet  Google Scholar 

  9. Engelfriet, J., Hoogeboom, H.J.: Tree-walking pebble automata. In: Jewels Are Forever, Contributions to Theoretical Computer Science in Honor of Arto Salomaa, pp. 72–83. Springer, Heidelberg (1999)

    Google Scholar 

  10. Engelfriet, J., Hoogeboom, H.J.: Automata with nested pebbles capture first-order logic with transitive closure. Log. Meth. in Comput. Sci. 3 (2007)

    Google Scholar 

  11. Fülöp, Z., Muzamel, L.: Weighted Tree-Walking Automata. Acta Cybernetica 19(2), 275–293 (2009)

    MathSciNet  Google Scholar 

  12. Globerman, N., Harel, D.: Complexity results for two-way and multi-pebble automata and their logics. Theoretical Computer Science 169(2), 161–184 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Neven, F., Schwentick, T.: On the power of tree-walking automata. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 547–560. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Samuelides, M., Segoufin, L.: Complexity of pebble tree-walking automata. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 458–469. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Schützenberger, M.P.: On the definition of a family of automata. Information and Control 4, 245–270 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  16. ten Cate, B., Segoufin, L.: Transitive closure logic, nested tree walking automata, and XPath. J. ACM (to appear, 2010); Short version in PODS 2008 (2008)

    Google Scholar 

  17. Thomas, W.: Classifying regular events in symbolic logic. Journal of Computer and System Sciences 25(3), 360–376 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  18. Trakhtenbrot, B.A.: Finite automata and logic of monadic predicates. Doklady Akademii Nauk SSSR 149, 326–329 (1961) (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LSV, ENS Cachan, CNRS & INRIA, France

    Benedikt Bollig, Paul Gastin, Benjamin Monmege & Marc Zeitoun

  2. LaBRI, Univ. Bordeaux & CNRS, France

    Marc Zeitoun

Authors
  1. Benedikt Bollig
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Gastin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Benjamin Monmege
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marc Zeitoun
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Samson Abramsky

  2. Université de Bordeaux (LaBRI) & INRIA, 351, cours de la Libération, 33405, Talence Cedex, France,

    Cyril Gavoille

  3. INRIA, Centre de Recherche Bordeaux – Sud-Ouest, 351 cours de la Libération, 33405, Talence Cedex, France

    Claude Kirchner

  4. Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Friedhelm Meyer auf der Heide

  5. University of Patras and RACTI, 26500, Patras, Greece

    Paul G. Spirakis

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bollig, B., Gastin, P., Monmege, B., Zeitoun, M. (2010). Pebble Weighted Automata and Transitive Closure Logics. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14162-1_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14161-4

  • Online ISBN: 978-3-642-14162-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation