Abstract
It is well known that one-dimensional cellular automata working on the usual neighborhood are Turing complete, and many acceleration theorems are known. However very little is known about the other neighborhoods. In this article, we prove that every one-dimensional neighborhood that is sufficient to recognize every Turing language is equivalent (in terms of real-time recognition) either to the usual neighborhood {–1,0,1} or to the one-way neighborhood {0,1}.
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References
Albert, J., Čulik II, K.: A simple universal cellular automaton and its one-way and totalistic version. Complex Systems 1, 1–16 (1987)
Choffrut, C., Čulik II, K.: On real-time cellular automata and trellis automata. Acta Informatica 21, 393–407 (1984)
Cole, S.N.: Real-time computation by n-dimensional iterative arrays of finite-state machines. IEEE Transactions on Computers C-18, 349–365 (1969)
Čulik, K., Hurd, L.P., Yu, S.: Computation theoretic aspects of cellular automata. Phys. D 45, 357–378 (1990)
Delorme, M., Mazoyer, J.: Reconnaissance parallèle des langages rationnels sur automates cellulaires plans. Theor. Comput. Sci. 281, 251–289 (2002)
Fischer, P.C.: Generation of primes by one-dimensional real-time iterative array. Journal of the Assoc. Comput. Mach. 12, 388–394 (1965)
Ibarra, O., Jiang, I.: Relating the power of cellular arrays to their closure properties. Theoretical Computer Science 57, 225–238 (1988)
Martin, B.: A universal automaton in quasi-linear time with its s-n-m form. Theoretical Computer Science 124, 199–237 (1994)
Mazoyer, J., Reimen, N.: A linear speed-up theorem for cellular automata. Theor. Comput. Sci. 101, 59–98 (1992)
Smith III, A.R.: Simple computation-universal cellular spaces. J. ACM 18, 339–353 (1971)
Smith III, A.R.: Real-time language recognition by one-dimensional cellular automata. Journal of the Assoc. Comput. Mach. 6, 233–253 (1972)
Terrier, V.: Language recognizable in real time by cellular automata. Complex Systems 8, 325–336 (1994)
Terrier, V.: Language not recognizable in real time by one-way cellular automata. Theoretical Computer Science 156, 281–287 (1996)
Terrier, V.: Two-dimensional cellular automata and their neighborhoods. Theor. Comput. Sci. 312, 203–222 (2004)
von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Urbana (1966)
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© 2005 Springer-Verlag Berlin Heidelberg
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Poupet, V. (2005). Cellular Automata: Real-Time Equivalence Between One-Dimensional Neighborhoods. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_11
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DOI: https://doi.org/10.1007/978-3-540-31856-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24998-6
Online ISBN: 978-3-540-31856-9
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