By M. Delorme (auth.), M. Delorme, J. Mazoyer (eds.)

ISBN-10: 9048151430

ISBN-13: 9789048151431

ISBN-10: 9401591539

ISBN-13: 9789401591539

Cellular automata will be considered either as computational types and modelling platforms of genuine tactics. This quantity emphasises the 1st point. In articles written through major researchers, subtle monstrous parallel algorithms (firing squad, lifestyles, Fischer's primes popularity) are handled. Their computational energy and the explicit complexity sessions they be sure are surveyed, whereas a few contemporary ends up in relation to chaos from a brand new dynamic platforms perspective also are offered. *Audience:* This publication can be of curiosity to experts of theoretical computing device technological know-how and the parallelism problem.

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**Additional info for Cellular Automata: A Parallel Model**

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Discrete parabolas and circles on 2D-cellular automata. To appear in Theoretical Computer Science. -C. How to simulate Turing machines by invertible one-dimensional cellular automata. 6 no. 4: 395-402, 1995. Durand B. Global properties of 2D-cellular automata. in Cellular Automata and Complex Systems, Goles E. and Martinez S. Eds, Kluwer, 1998. C. Generation ofprimes by a one dimensional real time iterative array. M. Vol. no. 12: 388-394, 1965. Gajardo A. Universality in a 2-dimensional cellular space with a neighborhood of cardinality 3.

In fact we consider uniform simulations in which there exist r and integers k and k' suchthat f(G~(c)) = G~(r(c)), and, in particular, the case where k = 1 ((R6ka, 1998)). r Figure 15. Another simulation: h-Simulation between cellular automata. Tothissimulation is also attached a notion of universal cellular automaton. A. Without any further hypothesis on r or on the configurations, we take the risk not to find any h-universal cellular automaton. So we have to be a little more precise. If we restriet the configurations to finite ones and if we demand r to be recursive, then we have examples.

Definition 3 Signals 1. A signal is a set { (! (t), t) heN, where f is a function from N into N such that (f(t + 1), t + 1) is (f(t) -1, t + 1), (f(t), t + 1) or (f(t)- 1, t + 1). Such a signal is said to be rightward (resp. leftward) ij, for each t, t E N, (f(t+1),t+1) E {(f(t),t+1), (f(t)+1,t+1)} (resp. {(f(t),t+ 1), (f(t)- 1, t + 1)}). 2. A signal is said to be simple or basic if the sequence (f(t+ 1)- f(t) )teN is ultimately periodic. We are interested in signals constructible by cellular automata.

### Cellular Automata: A Parallel Model by M. Delorme (auth.), M. Delorme, J. Mazoyer (eds.)

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