Outfix-Free Regular Languages and Prime Outfix-Free Decomposition

  • Yo-Sub Han
  • Derick Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3722)


A string x is an outfix of a string y if there is a string w such that x 1 wx 2=y, where x = x 1 x 2 and a set X of strings is outfix-free if no string in X is an outfix of any other string in X. We examine the outfix-free regular languages. Based on the properties of outfix strings, we develop a polynomial-time algorithm that determines the outfix-freeness of regular languages. We consider two cases: A language is given as a set of strings and a language is given by an acyclic deterministic finite-state automaton. Furthermore, we investigate the prime outfix-free decomposition of outfix-free regular languages and design a linear-time prime outfix-free decomposition algorithm for outfix-free regular languages. We demonstrate the uniqueness of prime outfix-free decomposition.


Regular Expression Regular Language Simple Path Prime Decomposition Decomposition Problem 
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  1. 1.
    Béal, M.-P., Crochemore, M., Mignosi, F., Restivo, A., Sciortino, M.: Computing forbidden words of regular languages. Fundamenta Informaticae 56(1-2), 121–135 (2003)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Clarke, C.L.A., Cormack, G.V.: On the use of regular expressions for searching text. ACM Transactions on Programming Languages and Systems 19(3), 413–426 (1997)CrossRefGoogle Scholar
  3. 3.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. McGraw-Hill Higher Education, New York (2001)zbMATHGoogle Scholar
  4. 4.
    Crochemore, M., Mignosi, F., Restivo, A.: Automata and forbidden words. Information Processing Letters 67(3), 111–117 (1998)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Czyzowicz, J., Fraczak, W., Pelc, A., Rytter, W.: Linear-time prime decomposition of regular prefix codes. International Journal of Foundations of Computer Science 14, 1019–1032 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Giammarresi, D., Montalbano, R.: Deterministic generalized automata. Theoretical Computer Science 215, 191–208 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Han, Y.-S., Trippen, G., Wood, D.: Simple-regular expressions and languages. In: Proceedings of DCFS 2005, pp. 146–157 (2005)Google Scholar
  8. 8.
    Han, Y.-S., Wang, Y., Wood, D.: Infix-free regular expressions and languages. To appear in International Journal of Foundations of Computer Science (2005)Google Scholar
  9. 9.
    Han, Y.-S., Wang, Y., Wood, D.: Prefix-free regular-expression matching. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 298–309. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Han, Y.-S., Wood, D.: The generalization of generalized automata: Expression automata. International Journal of Foundations of Computer Science 16(3), 499–510 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ito, M., Jürgensen, H., Shyr, H.-J., Thierrin, G.: N-prefix-suffix languages. International Journal of Computer Mathematics 30, 37–56 (1989)zbMATHCrossRefGoogle Scholar
  12. 12.
    Ito, M., Jürgensen, H., Shyr, H.-J., Thierrin, G.: Outfix and infix codes and related classes of languages. Journal of Computer and System Sciences 43, 484–508 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Jürgensen, H.: Infix codes. In: Proceedings of Hungarian Computer Science Conference, pp. 25–29 (1984)Google Scholar
  14. 14.
    Jürgensen, H., Konstantinidis, S.: Codes. In: Rozenberg, G., Salomaa, A. (eds.) Word, Language, Grammar. Handbook of Formal Languages, vol. 1, pp. 511–607. Springer, Heidelberg (1997)Google Scholar
  15. 15.
    Long, D.Y., Ma, J., Zhou, D.: Structure of 3-infix-outfix maximal codes. Theoretical Computer Science 188(1-2), 231–240 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Mateescu, A., Salomaa, A., Yu, S.: On the decomposition of finite languages. Technical Report 222, TUCS (1998)Google Scholar
  17. 17.
    Mateescu, A., Salomaa, A., Yu, S.: Factorizations of languages and commutativity conditions. Acta Cybernetica 15(3), 339–351 (2002)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Shyr, H.-J.: Lecture Notes: Free Monoids and Languages. Hon Min Book Company, Taichung (1991)Google Scholar
  19. 19.
    Wood, D.: Data structures, algorithms, and performance. Addison-Wesley Longman Publishing Co., Inc., Boston (1993)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yo-Sub Han
    • 1
  • Derick Wood
    • 1
  1. 1.Department of Computer ScienceThe Hong Kong University of Science and Technology 

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