Skip to main content

Finite Automata on Unranked and Unordered DAGs

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4588))

Abstract

We introduce linear expressions for unrestricted dags (directed acyclic graphs) and finite deterministic and nondeterministic automata operating on them. Those dag automata are a conservative extension of the T u,u -automata of Courcelle on unranked, unordered trees and forests. Several examples of dag languages acceptable and not acceptable by dag automata and some closure properties are given.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anantharaman, S., Narendran, P., Rusinowitch, M.: Closure properties and decision problems of dag automata. Information Processing Letters 94, 231–240 (2005)

    Article  MathSciNet  Google Scholar 

  2. Boneva, I., Talbot, J.-M.: Automata and logic for unranked and unordered trees. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 500–515. Springer, Heidelberg (2005)

    Google Scholar 

  3. Bossut, F., Dauchet, M., Warin, B.: A Kleene theorem for a class of planar acyclic graphs. Theor. Comp. Science Center Report HKUST-TCSC 2001-5 117, 251–265 (1995)

    MATH  MathSciNet  Google Scholar 

  4. Brüggemann-Klein, A., Murata, M., Wood, D.: Regular tree and hedge languages of unranked alphabets. Theor. Comp. Science Center Report HKUST-TCSC 2001 5, 29 (2001)

    Google Scholar 

  5. Charatonik, W.: Automata on dag representations of finite trees. Technical Report MPI-I-1999-2-001, MPI, Univ. Saarbrücken (1999)

    Google Scholar 

  6. Comon, H., Daucher, M., Gilleron, R., Tison, S., Tommasi, M.: Tree automata techniques and application. Available on the Web from 13ux02.univ-lille.fr in directoty tata (1998)

    Google Scholar 

  7. Courcelle, B.: A representation of graphs by algebraic expressions and its use for graph rewriting systems. In: Proc. 3rd Internat. Workshop on Graph-Grammars, pp. 112–132. Springer, Heidelberg (1988)

    Google Scholar 

  8. Courcelle, B.: On recognizable sets and tree automata. In: Aït-Kaci, H., Nivat, M. (eds.) Resolution of Equations in Algebraic Structures, vol. 1, pp. 93–126. Academic Press, London (1989)

    Google Scholar 

  9. Fanchon, J., Morin, R.: Regular sets of pomsets with auitoconcurrency. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 402–417. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Kamimura, T., Slutzki, G.: Parallel and two-way automata on directed ordered acyclic graphs. Inf. Control 49, 10–51 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kaminski, M., Pinter, S.: Finite automata on directed graphs. J. Comp. Sys. Sci. 44, 425–446 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  12. Menzel, J.R., Priese, L., Schuth, M.: Some examples of semi-rational dag languages. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 351–362. Springer Verlag, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Priese, L.: Semi-rational sets of dags. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 385–396. Springer Verlag, Heidelberg (2005)

    Google Scholar 

  14. Thomas, W.: Finite-state recognizability of graph properties. In: Krob, D. (ed.) Theorie des Automates et Applications, l’Universite de Rouen, France, vol. 172, pp. 147–159 (1992)

    Google Scholar 

  15. Thomas, W.: Automata theory on trees and partial orders. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, pp. 20–34. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Tero Harju Juhani Karhumäki Arto Lepistö

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Priese, L. (2007). Finite Automata on Unranked and Unordered DAGs. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73208-2_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73207-5

  • Online ISBN: 978-3-540-73208-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics