Abstract
The surjectivity problem for 2D cellular automata was proved undecidable in 1989 by Jarkko Kari. The proof consists in a reduction of a problem concerning finite tilings to this problem. This reduction uses a special and very sophisticated tile set. In this article, we present a much more simple tile set which can play the same role.
This work was partially supported by the Esprit Basic Research Action “Algebraic and Semantical Methods In Computer Science” and by the PRC “Mathématique et Informatique”.
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S. Amoroso and Y.N. Patt. Decision procedures for surjectivity and injectivity of parallel maps for tesselation structures. J. Comp. Syst. Sci., 6:448–464, 1972.
R. Berger. The undecidability of the domino problem. Memoirs of the American Mathematical Society, 66, 1966.
J. Kari. Reversibility and surjectivity problems of cellular automata. to appear in Journal of Computer and System Sciences.
J. Kari. Reversability of 2d cellular automata is undecidable. Physica, D 45:379–385, 1990.
E.F. Moore. Machine models of self-reproduction. Proc. Symp. Apl. Math., 14:13–33, 1962.
J. Myhill. The converse to Moore's garden-of-eden theorem. Proc. Am. Math. Soc., 14:685–686, 1963.
R.M. Robinson. Undecidability and nonperiodicity for tilings of the plane. Inventiones Mathematicae, 12:177–209, 1971.
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© 1993 Springer-Verlag Berlin Heidelberg
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Durand, B. (1993). Undecidability of the surjectivity problem for 2D cellular automata: A simplified proof. In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_16
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DOI: https://doi.org/10.1007/3-540-57163-9_16
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