Skip to main content
SpringerLink
Log in

On the Relationship between the McNaughton Families of Languages and the Chomsky Hierarchy

  • Conference paper
  • First Online:
Developments in Language Theory (DLT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2295))

Included in the following conference series:

Abstract

By generalizing the Church-Rosser languages the McNaughton families of languages are obtained. Here we concentrate on those families that are defined by monadic or special string-rewriting systems. We investigate the relationship of these families to each other and to the lower classes of the Chomsky hierarchy and present some closure and some non-closure properties for them. Moreover, we address some complexity issues for their membership problems.

Most of the work presented here was performed, while M. Holzer was visiting the Département d’I.R.O., Université de Montréal, Montréal, Québec, Canada.

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. M. Beaudry, M. Holzer, G. Niemann, and F. Otto. McNaughton languages. Mathematische Schriften Kassel 26/00, Universität Kassel, November 2000.A revised version will appear in Theoret. Comput. Sci.

    Google Scholar 

  2. L. Boasson and G. Sénizergues. NTS languages are deterministic and congruential. J. Comput. System Sci., 31:332–342, 1985.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. R.V. Book and F. Otto. String-Rewriting Systems. Springer-Verlag, NewYork, 1993.

    MATH  Google Scholar 

  5. G. Buntrock and F. Otto. Growing context-sensitive languages and Church-Rosser languages. Inform. and Comput., 141:1–36, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Buss. The Boolean formula value problem is in ALOGTIME. In Proc. of 19th STOC, pp. 123–131. ACM Press, 1987.

    Google Scholar 

  7. S.A. Cook and P. McKenzie. Problems complete for deterministic logarithmic space. J. Algorithms, 8:385–394, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  8. C. Herzog. Pushdown automata with bounded nondeterminism and bounded ambiguity. Theoret. Comput. Sci., 181:141–157, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Holzer and K.-J. Lange. On the complexities of linear LL(1) and LR(1) grammars. In Z. Ésik, editor, Proceedings 9th FCT, Lect. Notes Comput. Sci. 710, pp. 299–308. Springer-Verlag, Berlin, 1993.

    Google Scholar 

  10. J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, M.A., 1979.

    MATH  Google Scholar 

  11. D.S. Johnson. A catalog of complexity classes. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pp. 67–161. The MIT Press/Elsevier, Cambridge, MA/Amsterdam, 1990.

    Google Scholar 

  12. N.D. Jones and W.T. Laaser. Complete problems for deterministic polynomial time. Theoret. Comput. Sci., 3:105–117, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Lohrey. Private communication, November 2000.

    Google Scholar 

  14. K. Madlener, P. Narendran, F. Otto, and L. Zhang. On weakly confluent monadic stringrewriting systems. Theoret. Comput. Sci., 113:119–165, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  15. R. McNaughton, P. Narendran, and F. Otto. Church-Rosser Thue systems and formal languages. J. ACM, 35:324–344, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  16. P. Narendran. Church-Rosser and related Thue systems. PhD thesis, Rensselaer Polytechnic Institute, Troy, NewYork, 1984.

    Google Scholar 

  17. G. Niemann. Regular Languages and Church-Rosser congruential languages. In R. Freund and A. Kelemenová, editors, Grammar Systems 2000, Proceedings, pp. 359–370. Silesian University, Opava, 2000.

    Google Scholar 

  18. G. Niemann and J. Waldmann. Some regular languages that are Church-Rosser congruential. This volume.

    Google Scholar 

  19. G. Niemann and F. Otto. The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages. In M. Nivat, editor, Proceedings FoSSaCS’98, Lect. Notes Comput. Sci. 1378, pp. 243–257. Springer-Verlag, Berlin, 1998.

    Google Scholar 

  20. H. Sudborough. On the tape complexity of deterministic context-free languages. J. ACM, 25:405–414, 1978.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de mathématique et informatique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada

    M. Beaudry

  2. Institut für Informatik, Technische Universität München, Arcisstraβ21, 80290, München, Germany

    M. Holzer

  3. Fachbereich Mathematik/Informatik, Universität Kassel, 34109, Kassel, Germany

    G. Niemann & F. Otto

Authors
  1. M. Beaudry
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Holzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Niemann
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Otto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Algebra und Computermathematik Abt. für Theoretische Informatik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040, Wien, Austria

    Werner Kuich

  2. Department of Computer Science, Leiden University, P.O. Box 9512, 2300, RA Leiden, The Netherlands

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science, Lemminkaisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beaudry, M., Holzer, M., Niemann, G., Otto, F. (2002). On the Relationship between the McNaughton Families of Languages and the Chomsky Hierarchy. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_30

Download citation

  • DOI: https://doi.org/10.1007/3-540-46011-X_30

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43453-5

  • Online ISBN: 978-3-540-46011-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation