Deterministic regular languages

  • Anne Brüggemann-Klein
  • Derick Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

The ISO standard for Standard Generalized Markup Language (SGML) provides a syntactic meta-language for the definition of textual markup systems. In the standard the right hand sides of productions are called content models and they are based on regular expressions. The allowable regular expressions are those that are “unambiguous” as defined by the standard. Unfortunately, the standard's use of the term “unambiguous” does not correspond to the two well known notions, since not all regular languages are denoted by “unambiguous” expressions. Furthermore, the standard's definition of “unambiguous” is somewhat vague. Therefore, we provide a precise definition of “unambiguous expressions” and rename them deterministic regular expressions to avoid any confusion. A regular expression E is deterministic if the canonical ε-free finite automaton Me recognizing L(E) is deterministic. A regular language is deterministic if there is a deterministic expression that denotes it. We give a Kleene-like theorem for deterministic regular languages and we characterize them in terms of the structural properties of the minimal deterministic automata recognizing them. The latter result enables us to decide if a given regular expression denotes a deterministic regular language and, if so, to construct an equivalent deterministic expression.

Classification

Automata and formal languages esp. formal models in document processing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ASU86]
    Alfred V. Aho, Ravi Sethi, and Jeffrey D. Ullman. Compilers: Principles, Techniques, and Tools. Addison-Wesley Series in Computer Science, Addison-Wesley, Reading, Massachusetts, 1986.Google Scholar
  2. [BEG071]
    Ronald Book, Shimon Even, Sheila Greibach, and Gene Ott. Ambiguity in graphs and expressions. IEEE Transactions on Computers, C-20(2):149–153, February 1971.Google Scholar
  3. [Bru]
    Anne Brüggemann-Klein. Regular expressions into finite automata. To appear in the conference proceedings of Latin '92.Google Scholar
  4. [Brz64]
    Janusz A. Brzozowski. Derivatives of regular expressions. Journal of the ACM, 11(4):481–494, October 1964.Google Scholar
  5. [BS86]
    Gerard Berry and Ravi Sethi. From regular expressions to deterministic automata. Theoretical Computer Science, 48:117–126, 1986.Google Scholar
  6. [BW91]
    Anne Brüggemann-Klein and Derick Wood. On the expressive power of SGML document grammars. In preparation, 1991.Google Scholar
  7. [GH67]
    Seymour Ginsburg and Michael M. Harrison. Bracketed context-free languages. Journal of Computer and System Sciences, 1(1):1–23, March 1967.Google Scholar
  8. [Glu61]
    V.M. Glushkov. The abstract theory of automata. Russian Mathematical Surveys, 16:1–53, 1961.Google Scholar
  9. [Hen68]
    Frederick C. Hennie. Finite-State Models for Logical Machines. John Wiley, New York, 1968.Google Scholar
  10. [HU79]
    John E. Hopcroft and Jeffrey D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley Series in Computer Science, Addison-Wesley, Reading, Massachusetts, 1979.Google Scholar
  11. [ISO86]
    ISO 8879. Information processing—text and office systems—standard generalized markup language (SGML). October 1986. International Organization for Standardization.Google Scholar
  12. [LaL77]
    Wilf R. LaLonde. Regular right part grammars and their parsers. Communications of the ACM, 20(10):731–741, October 1977.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Anne Brüggemann-Klein
    • 1
  • Derick Wood
    • 2
  1. 1.Institut für InformatikUniversität FreiburgFreiburgGermany
  2. 2.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations