Abstract
We consider various TAG-like devices that generate one-way infinite words in real time. The simplest types of these devices are equivalent to iterative morphisms (also called substitutions), automatic sequences and iterative DGSM's. We consider also a few new types. Mainly we study the comparative power of these mechanisms and develop some techniques for proving that certain devices cannot produce a particular infinite word.
This work was done during the first author's stay at the University of Turku, Finland, supported by the Academy of Finland.
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References
J. P. Allouche, Finite Automata in 1-D and 2-D Physics, Number Theory & Physics, ed. by J. M. Luck, P. Moussa and M. Walschmidt, in: Springer Proceedings in Physics 47, Springer-Verlag (1990).
J. P. Allouche, J. Betrema and J. O. Shallit, Sur des Points Fixes de Morphismes d'un Monoide Libre, R.A.I.R.O., Informatique theorique et Applications 23, 3, 235–249 (1989).
J. P. Allouche and M. Mendes-France, Quasi-Crystal Using Chain and Automata Theory, J. Stat. Phys 42, 5/6 (1986).
J. M. Autebert and J. Gabarro, Iterated GSM's and Co-CFL, Acta Informatica 26, 749–769 (1989).
F. Axel, J. P. Allouche, M. Kleman, M. Mendes-France and J. Peyriere, Vibrational Modes in a One Dimensional ”Quasi-Alloy”: The Morse Case, Journal de Physique, Colloque C3, Suppl. 7, Tome 47 (1986).
J. Berstel, Properties of Infinite Words: Recent results, in: Lecture Notes in Computer Science 349, Springer-Verlag, New York (1989).
A. Cobham, Uniform tag Sequences, Math. Systems Theory 6, 164–192 (1972).
K. Culik II, Homomorphisms: Decidability, Equality and Test Sets, in: R. Book (ed.), Formal Language Theory, Perspectives and Open Problems, Academic Press, New York (1980).
K. Culik II and S. Dube, Balancing Order and Chaos in Image Generation, to appear in: ICALP Proceedings, Madrid (1991).
K. Culik II and T. Harju, The Ω-Sequence Equivalence Problem for D0L systems is Decidable, JACM 31, 277–298 (1984).
K. Culik II and J. Karhumäki, Iterative Devices Generating Infinite words, Tech. Report TR 9106, Univ. of South Carolina (1991).
K. Culik II, J. Karhumäki and A. Lepistö, Alternating Iteration of Morphisms and the Kolakovski Sequence, in: G. Rozenberg and A. Salomaa (eds.), A memorial volume for A. Lindenmayer, Springer-Verlarg (to appear).
K. Culik II and A. Salomaa, On Infinite Words Obtained by Iterating Morphisms, Theoret. Comput. Sci. 19, 29–38 (1982).
F. M. Dekking, Regularity and Irregularity of Sequences Generated by Automata, Sem. Th. de Nombres de Bordeaux, exp. 9 (1979–1980).
F. M. Dekking, On the Structure of Selfgenerating Sequences, Sem. Th. de Nombres de Bordeaux, (1980–1981).
A. Ehrenfeucht, K. P. Lee and G. Rozenberg, Subword Complexities of Various Classes of Deterministic Developmental Languages Without Interactions, Theoret. Comput. Sci. 1, 59–76 (1975).
P. C. Fischer, A. A. Meyer and A. L. Rosenberg, Time-restricted Sequence Generation, J. Comput. System Sci. 4, 50–73 (1970).
T. Harju and M. Linna, On the Periodicity of Morphisms in Free Monoids, R.A.I.R.O., Theoret. Inform. Appl. 20, 47–54 (1986).
J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA (1979).
W. Kolakovski, Self Generating Runs, problem 5304, American Math. Monthly 71 (1965), solution by N. Ucoluk, same journal 73, 681–682 (1966).
J. Karhumäki, Two Theorems Concerning Recognizable N-subsets of δ*. Theoretical Computer Science 1, 317–323 (1976).
C. Kimberling, Problem 6281*, Amer. Math. Monthly 86, 793 (1979).
D. Knuth, Solution to Problem E 2307, Amer. Math. Monthly 79, 773–774 (1972).
M. L. Minsky, Computation: Finite and Infinite Machines, Prentice-Hall, Englewood Cliffs, N.J. (1967).
J. J. Pansiot, Decidability of Periodicity for Infinite Words, R.A.I.R.O., Theoret. Inform. Appl. 20, 43–46 (1986).
P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, Berlin (1990).
G. Rozenberg and A. Salomaa, The Mathematicai Theory of L-Systems, Academic press, New York (1980).
A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series, Springer-Verlag, New York (1978).
J. Shallit, A Generalization of Automatic Sequences, Theoretical Computer Science 61, 1–16 (1988).
J. Shallit, Open Problem on the Kolakovski Sequence, (private communication).
A. R. Smith III, Plants, Fractals, and Formal Languages, Computer Graphics 18, 1–10 (1984).
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Culik, K., Karhumäki, J. (1992). Iterative devices generating infinite words. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_210
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DOI: https://doi.org/10.1007/3-540-55210-3_210
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