Abstract
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)...hn(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.
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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.
Correspondence with Karel Culik II during the early stages of the present work was helpful and encouraging.
This research was supported in part by Grants MCS-8003348 and MCS-8303922 of the National Science Foundation of the United States of America.
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References
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).
L. Boasson and M. Nivat, Adherences of languages, J. Computer and System Sciences 20(1980)285–309.
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.
K. Culik II and A. Salomaa, On infinite words obtained by iterating morphisms, Theor. Computer Science 19(1982)29–38.
T.Head, Adherences of DOL Languages, Theor. Computer Science, to appear in 1984.
G.T. Herman and G. Rosenberg, Developmental Systems and Languages (North Holland/American Elsevier, New York, 1975).
G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems (Academic Press, New York, 1980).
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© 1984 Springer-Verlag Berlin Heidelberg
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Head, T. (1984). Adherence equivalence is decidable for DOL languages. In: Fontet, M., Mehlhorn, K. (eds) STACS 84. STACS 1984. Lecture Notes in Computer Science, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12920-0_22
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DOI: https://doi.org/10.1007/3-540-12920-0_22
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