On Characterization of Attractor Basins of Fuzzy Multiple Attractor Cellular Automata

Article type: Research Article

Authors: Maji, Pradipta

Affiliations: Machine Intelligence Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700 108, India. E-mail: pmaji@isical.ac.in

Note: [] Address for corespondence: Machine Intelligence Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700 108, India

Abstract: Two new operators, namely, dependency vector (DV) and derived complement vector (DCV) are introduced in this paper to characterize the attractor basins of the additive fuzzy cellular automata (FCA) based associative memory, termed as fuzzy multiple attractor cellular automata (FMACA). The introduction of DV and DCV makes the complexity of the attractor basin identification algorithm linear in time. The characterization of the FMACA using DV and DCV establishes the fact that the FMACA provides both equal and unequal size of attractor basins. Finally, a set of algorithms is proposed to synthesize the FCA rules, attractors, and predecessors of attractors from the given DV and DCV in linear time complexity.

Keywords: Cellular automata, fuzzy cellular automata, associative memory, attractor basin

Journal: Fundamenta Informaticae, vol. 86, no. 1-2, pp. 143-168, 2008