Skip to main content
SpringerLink
Log in

Rewriting and tree automata

  • Conference paper
  • First Online:
Term Rewriting (TCS School 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 909))

Included in the following conference series:

Abstract

We summarize the main connections between rewriting, automata, and logical languages. We recall and illustrate from a rewriting point of view classical tree automata, Rabin and Büchi automata, which are associated with (W)SIS and (W)SkS logics. We introduce four recent classes of tree automata, closely linked to rewriting problems.

This work was partly supported by PRC-GDR “Mathématiques et Informatique”, by PRC project “Modèles logiques de la programmation”, and by ESPRIT Basic Research Action 6317 ASMICS 2.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aiken, A., D. Kozen, M. Vardi and E. L. Wimmers, The complexity of set constraints. Technical Report 93-1352, Computer Science Department, Cornell University, june 1993.

    Google Scholar 

  2. Bogaert, B. and S. Tison, Equality and disequality constraints on direct subterms in tree automata. Proceedings of STACS'92, Lecture Notes in Computer Science, Springer-Verlag, volume 577, pp. 161–171, 1992.

    Google Scholar 

  3. Brachman, R. J. What is Knowledge Representation, and where is it Going? Future Tendencies in Computer Science, Control and Applied Mathematics, Lecture Notes in Computer Science, Springer-Verlag, volume 653, pp. 189–203, 1992.

    Google Scholar 

  4. Büchi, J.R. The monadic theory of ω1. Decidable Theories II, Lecture Notes in Mathematics 328, Springer Verlag, Berlin, pp. 1–127, 1973.

    Google Scholar 

  5. Caron, A.-C., J.-L. Coquidé and M. Dauchet. Encompassment properties and automata with constraints. Proceedings of 5th Conference on Rewriting Techniques and Applications, Montréal (Canada), Lecture Notes in Computer Science, Springer Verlag, volume 690, pp. 328–342, june 1993.

    Google Scholar 

  6. Caron, A.-C, H. Comon, J.-L. Coquidé, M. Dauchet, F. Jacquemard. Pumping, Cleaning and Symbolic Constraints Solving, Proceedings of ICALP'94.

    Google Scholar 

  7. Comon, H. Unification et disunification. Théorie et applications. Ph. D. thesis. I.N.P. Grenoble, 1988.

    Google Scholar 

  8. Comon, H. Equational formulas on order-sorted algebras. Proceedings of ICALP'90, Lecture Notes in Computer Science, Springer-Verlag, volume 443, pp. 674–688, 1990.

    Google Scholar 

  9. Dauchet, M. and S. Tison. The Theory of Ground Rewrite Systems is Decidable. Proceedings of 5th IEEE Symposium on Logic in Computer Science (Philadelphia, PA.), IEEE Computer Society Press, pp. 242–248, june 1990.

    Google Scholar 

  10. Dauchet, M. and S. Tison. Structural complexity of classes of tree languages, Tree Automata and Languages, Elsevier Sciences, M. Nivat and A. Podelski ed., pp 327–353, 1992.

    Google Scholar 

  11. Dershowitz, N. and J.-P. Jouannaud. Rewrite systems. Handbook of Theoretical Computer Science, volume B, pp. 243–309. North-Holland, 1990.

    Google Scholar 

  12. Deruyver, A. VALERIAAN et EMMY: deux logiciels-laobratoires pour la réécriture, Ph.D., University of Lille I, 1990.

    Google Scholar 

  13. Gilleron, R., S. Tison and M. Tommasi. Solving Systems of Set Constraints with Negated Subset Relationships. Proceedings of 34th Symposium on Foundations of Computer Science (Palo Alto, CA.), IEEE Computer Society Press, pp. 372–380, november 1993.

    Google Scholar 

  14. Heintze, N. Set Based Program Analysis, Ph. D., Carnegie Mellon University, 1992.

    Google Scholar 

  15. Kucherov, G. and M. Tajin, Decidability of regularity and related properties of ground normal languages, 3rd International Workshop on Conditional Term Rewriting Systems, Lecture Notes in Computer Science, Springer-Verlag, vol. 652, PP. 272–286, 1992.

    Google Scholar 

  16. Litovsky, I., Y. Metivier and W. Zielonka. The power and limitations of local computations on graphs and networks. Lecture Notes in Computer Science, Springer Verlag, volume 657, pp. 333–343, 1993.

    Google Scholar 

  17. Rabin, M.O. Decidable Theories, Handbook of Mathematical Logic, North Holland Eds, pp. 595–627, 1977.

    Google Scholar 

  18. Thomas, W. Automata on Infinite Objects. Handbook of Theoretical Computer Science, volume B, pp. 135–192. North-Holland, 1990.

    Google Scholar 

  19. Vagvölgyi, S. and R. Gilleron, For a rewriting system it is decidable whether the set of irreductible ground terms is recognizable, Bulletin of EATCS, 48, pp. 197–209, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIFL, URA 369 CNRS, University of Lille I, 59655, Villeneuve d'Ascq, France

    Max Dauchet

Authors
  1. Max Dauchet
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hubert Comon Jean-Pierre Jounnaud

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dauchet, M. (1995). Rewriting and tree automata. In: Comon, H., Jounnaud, JP. (eds) Term Rewriting. TCS School 1993. Lecture Notes in Computer Science, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59340-3_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-59340-3_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59340-9

  • Online ISBN: 978-3-540-49237-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation