Maruoka, A. and Kimura, M., Injectivity and surjectivity of parallel maps for cellular automata, J. Comput. Syst. Sci., 18, 47--64 (1979).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....approach. Since then, for almost twenty years a quest for these generalizations to more than one dimension went on with little success. Invertibility and related properties for the one dimensional case were revisited in [54,87,14,29] Many equivalent characterizations of ica were given[90,47,48,35], but none that offered a finitary handle on invertibility. Finally, quite recently, Kari proved that Theorem 4.5 (Kari[38,39] There is no effective procedure for deciding whether or not an arbitrary two dimensional cellular automaton, given in terms of a local map, is invertible. His proof is ....

Maruoka, Akira, and Masayuki Kimura, "Injectivity and Surjectivity of Parallel Maps for Cellular Automata, " J. Comp. Syst. Sci. 18 (1979), 47--64.

....instance, 55, 7, 8, 10] to light a number of subtle issues somehow related to invertibility. But invertibility was explicitly addressed only in 1972, in seminal papers by Richardson[60] and Amoroso and Patt[2] 4 After that, theoretical work on invertibility in cellular automata proliferated[3, 61, 54, 46, 47, 48, 90, 35]. In spite of that work, however, for many years the most interesting ica actually exhibited remained an extremely simpleminded one (the longest orbit is of period two ) discovered by Patt through brute force enumeration[56] Ica continued to appear to be quite rare [2] Not only rare, but also ....

....approach. Since then, for almost twenty years a quest for these generalizations to more than one dimension went on with little success. Invertibility and related properties for the onedimensional case were revisited in [54, 87, 14, 29] Many equivalent characterizations of ica were given[90, 47, 48, 35], but none that offered a finitary handle on invertibility. Finally, quite recently, Kari proved that Theorem 4.5 (Kari[38, 39] There is no effective procedure for deciding whether or not an arbitrary twodimensional cellular automaton, given in terms of a local map, is invertible. His proof is ....

Maruoka, Akira, and Masayuki Kimura, "Injectivity and surjectivity of parallel maps for cellular automata," J. Comp. Syst. Sci. 18 (1979), 47--64.

....[39] have been studied, and all of them turned out to be universal. A reversible (or injective) CA (RCA) first appeared in the Garden of Eden problem (surjectivity problem of a global function) 31, 44] and then general properties concerning injectivity and surjectivity have been studied (e.g. [29, 30, 49]) Computing ability of RCA was first studied by Toffoli [53] He proved that every k dimensional irreversible CA can be simulated by a (k 1) dimensional RCA, from which computation universality of a 2 D RCA is derived. Later, Morita et al. strengthened his result showing that an RCA is ....

Maruoka, A. and Kimura, M., Injectivity and surjectivity of parallel maps for cellular automata, J. Comput. Syst. Sci., 18, 47--64 (1979).

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Maruoka, A. and Kimura, M., Injectivity and surjectivity of parallel maps for cellular automata, J. Comput. Syst. Sci., 18, 47--64 (1979).

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