Computations at the limit behaviour of cellular automata

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Oliveira, Pedro Paulo Balbi De
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Eis os objetivos originais, conforme literalmente listados no corpo do projeto: 1. To perform the detailed analysis of the very good rules in (Wolz and de Oliveira, 2008), in terms of their correlation with the notion of conservation degree defined in (Schranko and de Oliveira, 2010). In particular, to check whether the observation made in (Kari and Le Gloannec, 2012), about the proximity in Hamming distance between conservative rules in radius 3 space and good DCT rules, also holds for all 3000 very good rules found in (Wolz and de Oliveira, 2008). 2. To verify the validity of the present interpretation of conservation degree defined in (Schranko and de Oliveira, 2010), and to check whether a certain degree conservation is usually necessary in the problem- solving strategies represented by CA rules. Analogously, to reevaluate the notion of reversibility degree we previously proposed. 3. To attempt to conceive a procedure that would allow the derivation of the best possible DCT rules of radius 3 and, possibly, its generalisation to any space. 4. To tackle the problem of evaluating the existence of a solution of the parity problem in the radius 3 space, for odd-sized lattices. 5. To give the initial steps towards a theory of classification problems for CAs, at least for one-dimensional, binary rules. 6. To provide further developments of the template technique we introduced in (de Oliveira and Verardo, 2014a) and (de Oliveira and Verardo, 2014b) for representing CA rule families that share a given property. 7. To continue exploration of the limit behaviour of one-dimensional rules in terms of their spectral signatures. 8. To improve our approach to determining the limit behaviour of some elementary rules, both by conceiving an automated method for those currently obtained only manually, as well as devising a way to transform the ever- growing, redundant finite automata that characterise a limit set, into their equivalent, redundancy-free version. 9. To explore the possibility of setting up temporal combinations and spatial arrangements of CA rules in order to perform computational tasks, in particular in the context of classical benchmark problems.
cellular automata , emergent computation , classification problems , density classification , parity problem , limit behaviour
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