Abstract
Languages generated by monogenic (i.e. deterministic) context independent Lindenmayer systems (DOL systems) are investigated. Necessary and sufficient conditions are established under which the language generated by a DOL system is finite. Thus, sharp bounds on the cardinality of such a language are obtained. A feasible solution for the membership problem is given. The problems are solved of what is the minimum sized alphabet over which there is a DOL language of cardinality n and, conversely, what is the maximum sized finite DOL language over an alphabet of m letters. This in turn provides us with some number theoretic functions, interesting in their own right, of which several properties, interrelations and asymptotic approximations are derived.
This paper is registered at the Mathematical Center as IW 18/74.
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Keywords
- Decision Procedure
- Asymptotic Approximation
- Chinese Remainder Theorem
- Membership Problem
- Formal Language Theory
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References
See e.g. Knuth,D. Seminumerical algorithms. Addison-Wesley, Reading (Mass.)(1969), 256.
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Østerby, O. Prime decompositions with minimum sums. Univ. of Aarhus, Comp. Sci. Dept. Tech. Rept. DAIMI-PB 19 (1973).
Hardy, G.H. & Wright, E.M. An introduction to the theory of numbers, Oxford University Press (1945), 9–10.
Hardy & Wright. Op. cit. 9–10.
Østerby, Op. cit.
Landau, Op. cit.
Landau, Op. cit.
Hardy & Wright, Op. cit., 355.
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© 1974 Springer-Verlag Berlin Heidelberg
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Vitányi, P.M.B. (1974). On the size of dol languages. In: Rozenberg, G., Salomaa, A. (eds) L Systems. Lecture Notes in Computer Science, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06867-8_6
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DOI: https://doi.org/10.1007/3-540-06867-8_6
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