Skip to main content
SpringerLink
Log in

An Incremental Algorithm for Constructing Minimal Deterministic Finite Cover Automata

  • Conference paper
Implementation and Application of Automata (CIAA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3845))

Included in the following conference series:

  • 429 Accesses

Abstract

We present a fast incremental algorithm for constructing minimal DFCA for a given language. Since it was shown that the DFCA for a language L can have less states than the DFA for L, this technique seems to be the best choice for incrementally building the automaton for a large language, especially when the number of states in the DFCA is significantly less than the number of states in the corresponding minimal DFA. We have implemented the proposed algorithm and have tested it against the best known DFCA minimization technique.

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. Carrasco, R.C., Forcada, M.L.: Incremental construction and maintenence of minimal finite-state automata. Computational Linguistics 28(2), 207–216 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Daciuk, J., Mihov, S., Watson, B., Watson, R.E.: Incremental construction of minimal acyclic finite state automata. Computational Linguistics 26(1), 3–16 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Daciuk, J.: Comparison of construction algorithms for minimal, acyclic, deterministic, finite-state automata from sets of strings. In: Champarnaud, J.-M., Maurel, D. (eds.) CIAA 2002. LNCS, vol. 2608, pp. 255–261. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Mihov, S.: Direct construction of minimal acyclic finite states automata. Ann. de l’Université de Sofia “St. Kl. Ohridski”, Faculté de Mathematique et Informatique, Sofia, Bulgaria 92(2) (1998)

    Google Scholar 

  5. Sgarbas, K.N., Fakotakis, N.D., Kokkinakis, G.K.: Optimal insertion in deterministic DAWGs. Theoretical Computer Science 301 1(3), 103–117 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Sgarbas, K.N., Fakotakis, N.D., Kokkinakis, G.K.: Two algorithms for incremental construction of directed acyclic word graphs. International Journal on Artificial Intelligence Tools 4(3), 369–381 (1995)

    Article  Google Scholar 

  7. Watson, B.W.: A taxonomy of finite automata minimization algorithms. Eindhoven University of Technology, The Netherlands, Computing Science Note 93(44) (1993)

    Google Scholar 

  8. Watson, B.W.: Taxonomies and Toolkits of Regular Language Algorithms. Ph.D. thesis, Eindhoven University of Technology, the Netherlands (1995)

    Google Scholar 

  9. Watson, B.W.: An incremental DFA minimization algorithm. Finite State Methods in Natural Language Processing. In: ESSLLI Workshop, Helsinki, Finland, pp. 20–24 (August 2001)

    Google Scholar 

  10. Watson, B.W., Daciuk, J.: An efficient incremental DFA minimization algorithm. Natural Language Engineering 9(1), 49–64 (2003)

    Article  Google Scholar 

  11. Câmpeanu, C., Sântean, N., Yu, S.: Minimal cover-automata for finite languages. Theoretical Computer Science 267(1-2), 3–16 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Câmpeanu, C., Păun, A., Kari, L.: Results on transforming NFA into DFCA. Fundamenta Informaticae 64(1-4), 53–63 (2005)

    MathSciNet  MATH  Google Scholar 

  13. Câmpeanu, C., Păun, A.: Counting the number of minimal DFCA obtained by merging states. International Journal of Foundations of Computer Science 14(6), 995–1006 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Câmpeanu, C., Păun, A.: Lower bounds for NFA to DFCA transformations. In: Proceedings of DFCS 2004, London Ontario, Canada, pp. 121–130 (2004)

    Google Scholar 

  15. Körner, H.: A time and space efficient algorithm for minimizing cover automata for finite languages. International Journal of Foundations of Computer Science 14(6), 1071–1086 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Păun, A., Sântean, N., Yu, S.: An O(n 2) algorithm for minimal cover-automata for finite languages. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 243–251. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  17. Sântean, N.: Towards a Minimal Representation for Finite Languages: Theory and Practice. MSc thesis, Department of Computer Science, The University of Western Ontario, Canada (2000)

    Google Scholar 

  18. World Wide Web: The Grail+ project. A symbolic computation environment for finite-state machines, regular expressions, and finite languages (2002), http://www.csd.uwo.ca/Research/grail

  19. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  20. Salomaa, A.: Formal Languages. Academic Press, London (1973)

    MATH  Google Scholar 

  21. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. I, pp. 41–110. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  22. Câmpeanu, C., Păun, A., Yu, S.: An efficient algorithm for constructing minimal cover automata for finite languages. International Journal of Foundations of Computer Science 13(1), 83–98 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Information Technology, University of Prince Edward Island, Charlottetown, P.E.I., C1A 4P3, Canada

    Cezar Câmpeanu

  2. Department of Computer Science/Institute for Micromanufacturing, College of Engineering and Science, Louisiana Tech University, Ruston, P.O. Box 10348, Louisiana, LA-71272, USA

    Andrei Păun & Jason R. Smith

Authors
  1. Cezar Câmpeanu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrei Păun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jason R. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Sophia Antipolis, Laboratoire I3S, Les Algorithmes - bât. Euclide B, Université de Nice, 2000, route des lucioles, BP 121, 06903, Sophia Antipolis - Cedex, France

    Jacques Farré

  2. Sophia Antipolis, Ecole Polytechnique, Université de Nice, 930, route des colles, BP 145, 06903, Sophia Antipolis - Cedex, France

    Igor Litovsky

  3. Laboratoire I3S, Université de Nice, Sophia Antipolis & CNRS, France

    Sylvain Schmitz

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Câmpeanu, C., Păun, A., Smith, J.R. (2006). An Incremental Algorithm for Constructing Minimal Deterministic Finite Cover Automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds) Implementation and Application of Automata. CIAA 2005. Lecture Notes in Computer Science, vol 3845. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11605157_8

Download citation

  • DOI: https://doi.org/10.1007/11605157_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31023-5

  • Online ISBN: 978-3-540-33097-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation