Maruoka, A. and Kimura, M., Condition for injectivity of global maps for tessellation automata, Inf. Control, 32,158--162 (1976).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in [61] which brought 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 48,90,35]. In spite of that work, however, for many #4 Unbeknownst to those authors, systems that are in essence one dimensional cellular automata had already been studied in an abstract mathematical context by Hedlund and associates as early as 1963[30,31] both Richardson s results on invertibility ....

Maruoka, Akira, and Masayuki Kimura, "Conditions for Injectivity of Global Maps for Tessellation Automata," Info. Control 32 (1976), 158--162.

....is to say cl(P) S Z (where cl( Delta) is the topological closure operator) We have the following chain of relations S Z = cl(P) ae cl(F (S Z ) F (S Z ) ae S Z . We therefore conclude that F (S Z ) S Z which is contrary to our hypothesis. Proposition 2 (Maruoka and Kimura [11]) A 1 D CA is surjective iff it is k balanced for all k 2 N. A CA is k balanced if 8y 2 S 2r(k Gamma1) 1 ; fi fi Phi x 2 S 2rk 1 j f(x) y Psifi fi = S 2r ; where r is the radius. By Proposition 2, we can say that if a CA is chaotic then it has = 1 Gamma 1 S . The converse is ....

A. Maruoka and M. Kimura. Conditions for injectivity of global maps for tessellation automata. Information & control, 32:158--162, 1976.

....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 ....

Maruoka, Akira, and Masayuki Kimura, "Conditions for injectivity of global maps for tessellation automata," Info. Control 32 (1976), 158--162.

....4.3.1 A definition of Balancedness Recently, Christoph Durr et al. 21] raised the question about a definition of balancedness in the case of quantum ca. Here we give a generalization of the classical definition used by Amoroso and Patt [2] which differs from the one used by Maruoka and Kimura [38]) Definition 4.10 (Balanced qca) A qca F = hQ; f; Ni will be called balanced if and only if X x2Q N j hq; f(x)i j 2 = jQj jN j Gamma1 for every q 2 HQ , The following lemma shows the validity of this definition. Lemma 4.6 Every well formed qca F = hQ; f; Ni is balanced. Proof. If we take ....

Akira Maruoka and Masayuki Kimura. Condition for injectivity of global maps for tessellation automata. Information and Control, 32:158--162, 1976.

....[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., Condition for injectivity of global maps for tessellation automata, Inf. Control, 32,158--162 (1976).

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Maruoka, A. and Kimura, M., Condition for injectivity of global maps for tessellation automata, Inf. Control, 32,158--162 (1976).

No context found.

Maruoka A. and Kimura M. Condition for injectivity of global maps for tessellation automata. Inform.Control 32 (1976) 158-164.

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