Skip to main content
SpringerLink
Log in

Finding Finite Automata That Certify Termination of String Rewriting

  • Conference paper
Implementation and Application of Automata (CIAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3317))

Included in the following conference series:

Abstract

We present a technique based on the construction of finite automata to prove termination of string rewriting systems. Using this technique the tools Matchbox and TORPA are able to prove termination of particular string rewriting systems completely automatically for which termination was considered to be very hard until recently.

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. Book, R.V., Jantzen, M., Wrathall, C.: Monadic Thue systems. Theoret. Comput. Sci. 19, 231–251 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Book, R.V., Otto, F.: Cancellation rules and extended word problems. Inform. Process. Lett. 20, 5–11 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Book, R.V., Otto, F.: String-Rewriting Systems. In: Texts and Monographs in Computer Science. Springer, New York (1993)

    Google Scholar 

  4. Dershowitz, N.: Termination of linear rewriting systems. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 448–458. Springer, Heidelberg (1981)

    Google Scholar 

  5. Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting systems. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 449–459. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting systems. NIA Report 2003-09, National Institute of Aerospace, Hampton, VA, USA, Available at: http://research.nianet.org/~geser/papers/nia-matchbounded.html ; Accepted for Appl. Algebra Engrg. Comm. Comput.

  7. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Automated termination proofs with AProVE. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 210–220. Springer, Heidelberg (2004), Tool and description available at: http://www-i2.informatik.rwth-aachen.de/AProVE/

    Chapter  Google Scholar 

  8. Hibbard, T.N.: Context-limited grammars. J. ACM 21(3), 446–453 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hofbauer, D., Waldmann, J.: Deleting string rewriting systems preserve regularity. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710. Springer, Heidelberg (2003); Accepted for Theoret. Comput. Sci.

    Chapter  Google Scholar 

  10. Ravikumar, B.: Peg-solitaire, string rewriting systems and finite automata. In: Leong, H.-V., Jain, S., Imai, H. (eds.) ISAAC 1997. LNCS, vol. 1350, pp. 233–242. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  11. Tahhan Bittar, E.: Complexité linéaire du probléme de Zantema. C. R. Acad. Sci. Paris Sér. I Inform. Théor., t. 323, 1201–1206 (1996)

    MATH  MathSciNet  Google Scholar 

  12. Waldmann, J.: Matchbox: a tool for match-bounded string rewriting. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 85–94. Springer, Heidelberg (2004), Tool and description available at: http://theo1.informatik.uni-leipzig.de/matchbox/

    Chapter  Google Scholar 

  13. Zantema, H., Geser, A.: A complete characterization of termination of 0p1q → 1r0s. Appl. Algebra Engrg. Comm. Comput. 11(1), 1–25 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zantema, H.: Termination. In: Term Rewriting Systems, by Terese, pp. 181–259. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  15. Zantema, H.: TORPA: Termination of Rewriting Proved Automatically. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 95–104. Springer, Heidelberg (2004), Tool and description available at: http://www.win.tue.nl/~hzantema/torpa.html

    Chapter  Google Scholar 

  16. Zantema, H.: Termination of string rewriting proved automatically. Accepted for J. Automat. Reason. (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute of Aerospace, 144 Research Drive, Hampton, Virginia, 23666, USA

    Alfons Geser

  2. Mühlengasse 16, D-34125, Kassel, Germany

    Dieter Hofbauer

  3. Hochschule für Technik, Wirtschaft und Kultur (FH) Leipzig, Fb IMN, PF 30 11 66, D-04251, Leipzig, Germany

    Johannes Waldmann

  4. Department of Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Hans Zantema

Authors
  1. Alfons Geser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dieter Hofbauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Johannes Waldmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hans Zantema
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, MB, Canada

    Michael Domaratzki

  2. Department of Mathematics, University of Turku, Finland

    Alexander Okhotin

  3. School of Computing, Queen’s University, K7L 3N6, Kingston, Ontario, Canada

    Kai Salomaa

  4. Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Sheng Yu

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Geser, A., Hofbauer, D., Waldmann, J., Zantema, H. (2005). Finding Finite Automata That Certify Termination of String Rewriting. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30500-2_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24318-2

  • Online ISBN: 978-3-540-30500-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation