Fractal geometry, Turing machines and divide-and-conquer recurrences
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 28 (1994) no. 3-4, pp. 405-423.
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author = {Dube, S.},
title = {Fractal geometry, {Turing} machines and divide-and-conquer recurrences},
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Dube, S. Fractal geometry, Turing machines and divide-and-conquer recurrences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 28 (1994) no. 3-4, pp. 405-423. http://www.numdam.org/item/ITA_1994__28_3-4_405_0/

1. M. F. Barnsley, Fractals Everywhere, Academic Press, 1988. | MR | Zbl

2. J. L. Bentley, D. Haken and J. B. Saxe, A General Method for Solving Divide-and-Conquer Recurrences, SIGACT News, 1980, 12, pp. 36-44. | Zbl

3. L. Blum, M. Shub and S. Smale, On a Theory of Computation and Complexity over the Real Numbers: NP Completeness, recursive functions and universal machines, Bulletin of American Mathematical Society, 1989, 21, pp. 1-46. | MR | Zbl

4. T. H. Cormen, C. E. Leiserson and R. L. Rivest, Introduction to Algorithms, MIT Press, 1990. | MR | Zbl

5. K. Culik Ii and S. Dube, Affine Automata and Related Techniques for Generation of Complex Images, Theoretical Computer Science, 1993, 116, pp. 373-398. | MR | Zbl

6. K. Culik Ii and S. Dube, Encoding Images as Words and Languages, International Journal of Algebra and Computation, 1993, 3, No. 2, pp. 211-236. | MR | Zbl

7. S. Dube, Undecidable Problems in Fractal Geometry, Technical Report 93-71, Dept. of Math. and Comp. Sci., University of New England at Armidale, Australia. | MR

8. S. Dube, Using Fractal Geometry for Solving Divide-and-Conquer Recurrences, to appear in Journal of Aust. Math. Soc., Applied Math., Preliminary version in Proc. of ISAAC'93, Hong Kong. Lecture Notes in Computer Science, Springer-Verlag, 762, pp. 191-200. | MR | Zbl

9. K. J. Falconer, Digital Sun Dials, Paradoxical Sets and Vitushkin's Conjecture, Math Intelligencer, 1987, 9, pp. 24-27. | Zbl

10. J. Gleick, Chaos-Making a New Science, Penguin Books, 1988. | MR | Zbl

11. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1979. | MR | Zbl

12. J. Hutchinson, Fractals and Self-similarity, Indiana University Journal of Mathematics, 1981, 30, pp. 713-747. | MR | Zbl

13. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, 1982. | MR | Zbl

14. R. Penrose, The Emperor's New Mind, Oxford University Press, Oxford, 1990. | Zbl