Abstract
The limit set of a CA contains all configurations that can appear after arbitrarily long computations. In this article decision problems of type “Given a CA.A, does the limit set of A have property P” are studied for different properties P. It turns out that such problems are undecidable for all non-trivial properties P.
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References
Amoroso, S. and Patt, Y.: 1972, ‘Decision procedures for surjectivity and injectivity’, Journal of Computer and System Sciences, 6, 448.
Conley, C.: 1978, ‘Isolated invariant sets and the Morse index’, CBMS Regional Conference Series 38, Am. Math. Soc., Providence, RI
Culik, K., Hurd, L. and Yu, S.: 1990a, ‘Computation theoretic aspects of cellular automata’, Physica D, 45, 357.
Culik, K., Hurd, L. and Yu, S.: 1990b, ‘Formal languages and global cellular automaton behavior’, Physica D, 45, 396.
Culik, K., Pachl, J. and Yu, S.: 1989, ‘On the limit sets of cellular automata’, SIAM Journal on Computing, 18, 831.
Hurd, L.: 1987, ‘Formal language characterizations of cellular automaton limit sets’, Complex Systems, 1, 69.
Hurd, L.: 1990, ‘Recursive cellular-automata invariant sets’, Complex Systems, 4, 119.
Hurley, M.: 1990a, ‘Attractors in cellular automata’, Ergodic Theory and Dynamical Systems, 10, 131.
Hurley, M.: 1990b, ‘Ergodic aspects of cellular automata’, Ergodic Theory and Dynamical Systems, 10, 671.
Hurley, M.: 1991, ‘Varieties of periodic at tractor in cellular automata’, Transactions of the American Mathematical Society, 326, 701.
Kari, J.: 1992a, ‘The nilpotency problem of one-dimensional cellular automata’, SIAM Journal on Computing, to appear.
Kari, J.: 1992b, ‘Reversibility and surjectivity problems of cellular automata’, Journal of Computer and System Sciences, to appear.
Kari, J.: 1992c, ‘Rice’s theorem for the limit sets of cellular automata’, Theoretical Computer Science, submitted.
Podkolzin, A.: 1976, ‘O povedenijah odnorodnijh struktor’, Problemy Kibernetiky, (in russian) 31, 133.
Wolfram, S.: 1984, ‘Computation theory of cellular automata’, Communications in Mathematical Physics, 96, 15.
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© 1993 Springer Science+Business Media Dordrecht
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Kari, J. (1993). Properties of Limit Sets of Cellular Automata. In: Boccara, N., Goles, E., Martinez, S., Picco, P. (eds) Cellular Automata and Cooperative Systems. NATO ASI Series, vol 396. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1691-6_25
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DOI: https://doi.org/10.1007/978-94-011-1691-6_25
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4740-1
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