Evolving Sequential Combinations of Elementary Cellular Automata Rules
Performing computations with cellular automata, individually or arranged in space or time, opens up new conceptual issues in emergent, artificial life type forms of computation, and opens up the possibility of novel technological advances. Here, a methodology for combining sequences of elementary cellular automata is presented, in order to perform a given computation. The problem at study is the well-known density classification task that consists of determining the most frequent bit in a binary string. The methodology relies on an evolutionary algorithm, together with analyses driven by background knowledge on dynamical behaviour of the rules and their parametric estimates, as well as those associated with the formal behaviour characterisation of the rules involved. The resulting methodology builds upon a previous approach available in the literature, and shows its efficacy by leading to 2 rule combinations already known, and to additional 26, apparently unknown so far.
Unable to display preview. Download preview PDF.
- Kanoh, Wu, Y.: Evolutionary design of rule changing cellular automata. In: Palade, V., Howlett, R.J., Jain, L. (eds.) KES 2003. LNCS, vol. 2773, pp. 258–264. Springer, Heidelberg (2003), www.kslab.is.tsukuba.ac.jp/kanoh/kslab/study2/kanoh_KES2003.pdf CrossRefGoogle Scholar
- Lee, K.M., Xu, H., Chau, H.F.: Parity problem with a cellular automaton solution. Physical Review E 64, 026702/1–026702/4 (2001)Google Scholar
- Mitchell, M., Crutchfield, J.P., Das, R.: Evolving cellular automata to perform computations. In: Back, T., Fogel, D., Michalewicz, Z. (eds.) Handbook of Evolutionary Computation. Oxford University Press, Oxford (1998)Google Scholar
- de Oliveira, P.P.B., Vaiano, R.B.: Searching for a cellular automaton to solve the parity problem (in Portuguese). Unpublished manuscript under review (2005)Google Scholar
- Li, W.: Parameterizations of Cellular Automata Rule Space. SFI Technical Report: Preprints, Santa Fe, NM, USA (1991)Google Scholar
- Mitchell, M.: An Introduction to Genetic Algorithms. Bradford Book, Reprint edition (1998)Google Scholar
- Mitchell, M.: Computation in cellular automata: A selected review. In: Nonstandard Computation. VCH Verlagsgesellschaft, Weinheim (1996)Google Scholar