Computations at the limit behaviour of cellular automata
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Projeto de Pesquisa
Date
2017-03-28
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Authors
Oliveira, Pedro Paulo Balbi De
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Abstract
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.
Description
Keywords
cellular automata , emergent computation , classification problems , density classification , parity problem , limit behaviour