Deterministic regular languages

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


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 M e 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.


Automata and formal languages esp. formal models in document processing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 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

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