Skip to main content
SpringerLink
Log in

Computing the Follow Automaton of an Expression

  • 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

Small nondeterministic recognizers are very useful in practical applications based on regular expression searching. The follow automaton, recently introduced by Ilie and Yu, is such a small recognizer, since it is a quotient of the position automaton. The aim of this paper is to present an efficient computation of this quotient, based on specific properties of the \(\mathcal{ZPC}\) of the expression. The motivation is twofold. Since this structure is already a basic tool for computing the position automaton, Antimirov’s automaton and Hromkovic’s automaton, the design of an algorithm for computing the follow automaton via this structure makes it easier to compare all these small recognizers. Secondly such an algorithm provides a straightforward alternative to the rather sophisticated handling of ε-transitions used in the original algorithm.

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. Antimirov, V.: Partial derivatives of regular expressions and finite automaton constructions. Theoret. Comput. Sci. 155, 291–319 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brüggemann-Klein, A.: Regular Expressions into Finite Automata, Theoret. Comput. Sci. 120, 197–213 (1993)

    MATH  Google Scholar 

  3. Champarnaud, J.-M.: Subset Construction Complexity for Homogeneous Automata, Position Automata and ZPC-Structures. Theoret. Comput. Sci. 267, 17–34 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Champarnaud, J.-M., Ziadi, D.: Computing the Equation Automaton of a Regular Expression in O(s2) Space and Time. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 157–168. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  5. Champarnaud, J.-M., Ziadi, D.: From c-continuations to new quadratic algorithms for automaton synthesis. Intern. Journ. of Alg. and Comp. 11(6), 707–735 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Champarnaud, J.-M.: Evaluation of three implicit structures to implement nondeterministic automata from regular expressions. Intern. J. of Foundations of Comp. Sc. 13(1), 99–113 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chang, C.-H., Paige, R.: From Regular Expressions to DFA’s Using Compressed NFA’s. Theoret. Comput. Sci. 178, 1–36 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Glushkov, V.M.: The Abstract Theory of Automata. Russian Math. Surveys 16, 1–53 (1961)

    Article  Google Scholar 

  9. Hagenah, C., Muscholl, A.: Computing ε-free NFAs from regular expressions in O(n log2(n)) time. Theoret. Inform. Appl. 34(4), 257–277 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hromkovic, J., Seibert, S., Wilke, T.: Translating regular expressions into small ε-free nondeterministic finite automata. J. Comput. System Sci. 62(4), 565–588 (2001)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  12. Ilie, L., Yu, S.: Constructing NFAs by optimal use of positions in regular expressions. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 279–288. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Ilie, L., Yu, S.: Algorithms for Computing Small NFAs. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 328–340. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. McNaughton, R., Yamada, H.: Regular Expressions and State Graphs For Automata. IEEE Trans. on Electronic Computers 9(1), 39–47 (1960)

    Article  Google Scholar 

  15. Ponty, J.-L., Ziadi, D., Champarnaud, J.-M.: A new Quadratic Algorithm to Convert a Regular Expression into an Automaton. In: Raymond, D.R., Yu, S., Wood, D. (eds.) WIA 1996. LNCS, vol. 1260, pp. 109–110. Springer, Heidelberg (1997)

    Google Scholar 

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

    Google Scholar 

  17. Ziadi, D., Ponty, J.-L., Champarnaud, J.-M.: Passage d’une expression rationnelle à un automate fini non-déterministe. Journées Montoises (1995); Bull. Belg. Math. Soc. 4, 177–203 (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. L.I.F.A.R, Université de Rouen,  

    Jean-Marc Champarnaud, Florent Nicart & Djelloul Ziadi

  2. XRCE, Xerox Research Center Europe, 38240, Meylan

    Florent Nicart

Authors
  1. Jean-Marc Champarnaud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Florent Nicart
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Djelloul Ziadi
    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

Champarnaud, JM., Nicart, F., Ziadi, D. (2005). Computing the Follow Automaton of an Expression. 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_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30500-2_9

  • 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