Skip to main content
SpringerLink
Log in

Decision Problems for Language Equations with Boolean Operations

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

Included in the following conference series:

Abstract

The paper studies resolved systems of language equations that allow the use of all Boolean operations in addition to concatenation. Existence and uniqueness of solutions are shown to be their nontrivial properties, these properties are given characterizations by first order formulae, and the position of the corresponding decision problems in the arithmetical hierarchy is determined. The class of languages defined by components of unique solutions of such systems is shown to coincide with the class of recursive languages.

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. J. Autebert, J. Berstel and L. Boasson, “Context-Free Languages and Pushdown Automata”, Handbook of Formal Languages, Vol. 1, 111–174, Springer-Verlag, Berlin, 1997.

    MathSciNet  Google Scholar 

  2. N. Immerman, Descriptive complexity, Springer-Verlag, New York, 1998.

    Google Scholar 

  3. W. Kuich, “Semirings and Formal Power Series: Their Relevance to Formal Language and Automata”, Handbook of Formal Languages, Vol. 1, 609–677, Springer-Verlag, Berlin, 1997.

    MathSciNet  Google Scholar 

  4. E._L. Leiss, Language equations, Springer-Verlag, New York, 1999.

    MATH  Google Scholar 

  5. A. Okhotin, “Conjunctive grammars”, Journal of Automata, Languages and Combinatorics, 6:4 (2001), 519–535.

    MATH  MathSciNet  Google Scholar 

  6. A. Okhotin, “Conjunctive grammars and systems of language equations”, Programming and Computer Software, 28:5 (2002) 243–249.

    Article  MATH  MathSciNet  Google Scholar 

  7. Ch. H. Papadimitriou, Computational complexity, Addison-Wesley, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing, Queen’s University, Kingston, Ontario, Canada, K7L3N6

    Alexander Okhotin

Authors
  1. Alexander Okhotin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Okhotin, A. (2003). Decision Problems for Language Equations with Boolean Operations. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-45061-0_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation