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Generalized One-Unambiguity

  • Pascal Caron
  • Yo-Sub Han
  • Ludovic Mignot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)

Abstract

Brüggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E) = L and the position automaton of E is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (n + 2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.

Keywords

Regular Expression Transverse Property Regular Language Closure Property Sink State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Blum, N.: An O(n logn) implementation of the standard method for minimizing n-state finite automata. Inform. Process. Lett. 57(2), 65–69 (1996)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bray, T., Paoli, J., Sperberg-Mc Queen, C.M., Maler, E., Yergeau, F.: Extensible Markup Language (XML) 1.0, 4th edn. (2006), http://www.w3.org/TR/2006/REC-xml-20060816
  3. 3.
    Brüggemann-Klein, A., Wood, D.: One-unambiguous regular languages. Inform. Comput. 140, 229–253 (1998)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Gelade, W.: Succinctness of regular expressions with interleaving, intersection and counting. Theor. Comput. Sci. 411(31-33), 2987–2998 (2010)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Gelade, W., Neven, F.: Succinctness of the complement and intersection of regular expressions. In: Albers, S., Weil, P. (eds.) STACS. Dagstuhl Seminar Proceedings, vol. 08001, pp. 325–336 (2008)Google Scholar
  6. 6.
    Glushkov, V.M.: The abstract theory of automata. Russian Mathematical Surveys 16, 1–53 (1961)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Hopcroft, J.E.: An n log n algorithm for minimizing the states in a finite automaton. In: Kohavi, Z. (ed.) The Theory of Machines and Computations, pp. 189–196. Academic Press, New York (1971)Google Scholar
  8. 8.
    Kleene, S.: Representation of events in nerve nets and finite automata. In: Automata Studies, Ann. Math. Studies, vol. 34, pp. 3–41. Princeton U. Press (1956)Google Scholar
  9. 9.
    McNaughton, R.F., Yamada, H.: Regular expressions and state graphs for automata. IEEE Transactions on Electronic Computers 9, 39–57 (1960)CrossRefMATHGoogle Scholar
  10. 10.
    Moore, E.F.: Gedanken experiments on sequential machines. In: Automata Studies, pp. 129–153. Princeton Univ. Press, Princeton (1956)Google Scholar
  11. 11.
    Myhill, J.: Finite automata and the representation of events. WADD, TR-57-624, 112–137 (1957)Google Scholar
  12. 12.
    Nerode, A.: Linear automata transformation. In: Proceedings of AMS, vol. 9, pp. 541–544 (1958)Google Scholar
  13. 13.
    Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. 3(2), 115–125 (1959)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pascal Caron
    • 1
  • Yo-Sub Han
    • 2
  • Ludovic Mignot
    • 1
  1. 1.LITISUniversité de RouenSaint-Étienne du Rouvray CedexFrance
  2. 2.Dept. of Computer ScienceYonsei UniversitySeoulRepublic of Korea

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