Skip to main content
SpringerLink
Log in
Book cover

International Conference on Developments in Language Theory

DLT 2013: Developments in Language Theory pp 289–300Cite as

Alternative Automata Characterization of Piecewise Testable Languages

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7907))

Abstract

We present a transparent condition on a minimal automaton which is equivalent to piecewise testability of the corresponding regular language. The condition simplifies the original Simon’s condition on the minimal automaton in a different way than conditions of Stern and Trahtman. Secondly, we prove that every piecewise testable language L is k-piecewise testable for k equal to the depth of the minimal DFA of L. This result improves all previously known estimates of such k.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Almeida, J.: Implicit operations on finite \(\mathcal J\)-trivial semigroups and a conjecture of I. Simon. J. Pure Appl. Algebra 69, 205–218 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Higgins, P.: A proof of Simon’s theorem on piecewise testable languages. Theoret. Comput. Sci. 178, 257–264 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jirásková, G., Klíma, O.: Descriptional complexity of biautomata. In: Kutrib, M., Moreira, N., Reis, R. (eds.) DCFS 2012. LNCS, vol. 7386, pp. 196–208. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Klíma, O.: Piecewise testable languages via combinatorics on words. Discrete Mathematics 311, 2124–2127 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Klíma, O., Polák, L.: Biautomata for k-piecewise testable languages. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 344–355. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  6. Pin, J.-E.: Syntactic semigroups. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, ch. 10. Springer (1997)

    Google Scholar 

  7. Pin, J.-E.: Varieties of Formal Languages. North Oxford Academic, Plenum (1986)

    Google Scholar 

  8. Simon, I.: Hierarchies of events of dot-depth one. Ph.D. thesis. U. Waterloo (1972), http://maveric.uwaterloo.ca/~brzozo/phd.html

  9. Simon, I.: Piecewise testable events. In: Brakhage, H. (ed.) ICALP 1975. LNCS, vol. 33, pp. 214–222. Springer, Heidelberg (1975)

    Google Scholar 

  10. Stern, J.: Complexity of some problems from the theory of automata. Information and Control 66, 163–176 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  11. Straubing, H., Thérien, D.: Partially ordered finite monoids and a theorem of I. Simon. J. Algebra 119, 393–399 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  12. Trahtman, A.N.: Piecewise and local threshold testability of DFA. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 347–358. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Ondřej Klíma & Libor Polák

Authors
  1. Ondřej Klíma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Libor Polák
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LIGM, University Paris-Est Marne-la-Vallée, 5 Bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France

    Marie-Pierre Béal

  2. LIAFA, UMR 7089, University Paris Diderot, 75205, Paris cedex 13, France

    Olivier Carton

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Klíma, O., Polák, L. (2013). Alternative Automata Characterization of Piecewise Testable Languages. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38771-5_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38770-8

  • Online ISBN: 978-3-642-38771-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation