Skip to main content
SpringerLink
Log in

Walking on Data Words

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

Data words are words with additional edges that connect pairs of positions carrying the same data value. We consider a natural model of automaton walking on data words, called Data Walking Automaton, and study its closure properties, expressiveness, and the complexity of some basic decision problems. Specifically, we show that the class of deterministic Data Walking Automata is closed under all Boolean operations, and that the class of non-deterministic Data Walking Automata has decidable emptiness, universality, and containment problems. We also prove that deterministic Data Walking Automata are strictly less expressive than non-deterministic Data Walking Automata, which in turn are captured by Class Memory Automata.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Björklund, H., Schwentick, T.: On notions of regularity for data languages. Theor. Comput. Sci. 411(4-5), 702–715 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bojańczyk, M., Colcombet, T.: Tree-walking automata cannot be determinized. Theor. Comput. Sci. 350(2-3), 164–173 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bojańczyk, M., Colcombet, T.: Tree-walking automata do not recognize all regular languages. SIAM J. 38(2), 658–701 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bojańczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data words. ACM Trans. Comput. Log. 12(4), 27 (2011)

    MathSciNet  MATH  Google Scholar 

  5. Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data trees and XML reasoning. J. Assoc. Comput. Mach. 56(3) (2009)

  6. Engelfriet, J., Hoogeboom, H.: Tree-walking pebble automata. In: Jewels are forever, contributions to Theoretical Computer Science in honor of Arto Salomaa, pp 72–83. Springer (1999)

  7. Holzer, M., Kutrib, M.: Descriptional and computational complexity of finite automata: a survey. Inf. Comput. 209(3), 456–470 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329–363 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kara, A., Schwentick, T., Zeume, T.: Temporal logics on words with multiple data values. In: Proceedings of the IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), pp. 481–492.Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2010)

  10. Libkin, L., Vrgoc, D.: Regular expressions for data words. In: Proceedings of the 18th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), LNCS, vol. 7180, pp 274–288. Springer (012)

  11. Manuel, A., Zeume, T.: Two-variable logic on 2-dimensional structures. In: Proceedings of the 22th EACSL Annual Conference on Computer Science Logic (CSL), LIPIcs, vol. 23, pp. 484–499. Schloss Dagstuhl -Leibniz-Zentrum fuer Informatik (2013)

  12. McNaughton, R., Papert, S.: Counter-free automata. MIT (1971)

  13. Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log. 5(3), 403–435 (2004)

    Article  MathSciNet  Google Scholar 

  14. Rabin, M., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3(2), 114–125 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  15. Schwentick, T., Zeume, T.: Two-variable logic with two order relations. In: Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL), LNCS, vol. 6247, pp 499–513. Springer (2010)

  16. Sipser, M.: Halting space-bounded computations. Theor. Comput. Sci. 10, 335–338 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  17. Thomas, W.: Elements of an automata theory over partial orders. In: Partial Order Methods in Verification, pp 25–40. American Mathematical Society (1997)

  18. Vollmer, H.: Introduction to Circuit Complexity: a uniform approach. Texts in Theoretical Computer Science. An EATCS Series. Springer (1999)

Download references

Acknowledgments

The first author thanks Thomas Colcombet for detailed discussions and acknowledges that some of the ideas were inspired during these. The second author acknowledges Mikołaj Bojańczyk and Thomas Schwentick for detailed discussions about the relationship between DWA and Data Automata. The authors are also grateful to the anonymous referees for the many helpful remarks on the paper.

Author information

Authors and Affiliations

  1. LIAFA, University of Paris Diderot, Paris, France

    Amaldev Manuel

  2. LaBRI, University of Bordeaux, Bordeaux, France

    Anca Muscholl

  3. CNRS / LaBRI, University of Bordeaux, Bordeaux, France

    Gabriele Puppis

Authors
  1. Amaldev Manuel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anca Muscholl
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gabriele Puppis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gabriele Puppis.

Additional information

This research has received funding from the ANR project 2010 BLANC 0202 01 FREC and from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement n. 259454.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manuel, A., Muscholl, A. & Puppis, G. Walking on Data Words. Theory Comput Syst 59, 180–208 (2016). https://doi.org/10.1007/s00224-014-9603-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-014-9603-3

Keywords

Search

Navigation