Adherence equivalence is decidable for DOL languages

  • Tom Head
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)


A procedure is given for deciding whether or not the languages generated by an arbitrary pair of DOL systems have the same adherence.

From arbitrary DOL systems simpler systems are constructed which have the same adherences as the original systems. Representations of the sequences in the adherences of these simpler systems are constructed. Such sequences either have the form uvω for finite strings u and v or they have a form widely discussed by A.Salomaa: wsh(s)h2(s) ... where h is an endomorphism of A⋆ and h(w)=ws. The problem of deciding equality of two sequences of the latter type was recently solved by K.Culik II and T.Harju and their algorithm is a major tool used here.


Finite Collection Empty String Prefix Code Finite String Elementary String 
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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  1. [1]
    J. Beauquier and M. Nivat, Application of formal language theory to problems of security and synchronization, in: R.V. Book, Ed., Formal Language Theory (Academic Press, New York, 1980).Google Scholar
  2. [2]
    L. Boasson and M. Nivat, Adherences of languages, J. Computer and System Sciences 20(1980)285–309.Google Scholar
  3. [3]
    K.Culik II and T.Harju, The ω-sequence equivalence problem for DOL systems is decidable, J. Assoc. Computing Machinery, to appear; see also: Proc. 13th ACM Symposium on the Theory of Computing (1981)1–6.Google Scholar
  4. [4]
    K. Culik II and A. Salomaa, On infinite words obtained by iterating morphisms, Theor. Computer Science 19(1982)29–38.Google Scholar
  5. [5]
    T.Head, Adherences of DOL Languages, Theor. Computer Science, to appear in 1984.Google Scholar
  6. [6]
    G.T. Herman and G. Rosenberg, Developmental Systems and Languages (North Holland/American Elsevier, New York, 1975).Google Scholar
  7. [7]
    G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems (Academic Press, New York, 1980).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Tom Head
    • 1
  1. 1.Department of Mathematical SciencesUniversity of AlaskaFairbanksUSA

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