Asynchronous cellular automata and pattern classification

Abstract

This paper designs an efficient two-class pattern classifier utilizing asynchronous cellular automata (ACAs). The two-state three-neighborhood one-dimensional ACAs that converge to fixed points from arbitrary seeds are used here for pattern classification. To design the classifier, we first identify a set of ACAs that always converge to fixed points from any seeds with following properties -(1) each ACA should have at least two but not huge number of fixed point attractors, and (2) the convergence time of these ACAs are not to be exponential. In order to address the first issue, we propose a graph, coined as fixed point graph of an ACA that facilitates in counting the fixed points. We further perform an experimental study to estimate the convergence time of ACAs, and find that there are some convergent ACAs which demand exponential convergence time. Finally, we find that there are 71 (out of 256) ACAs which can be effective candidates as pattern classifier. We use each of the candidate ACAs on some standard data sets, and observe the effectiveness of each ACAs as pattern classifier. It is observed that the proposed classifier is very competitive and performs reliably better than many standard existing algorithms.

Asynchronous Cellular Automata

“…As an example of a possible application of the use of these dynamical systems, we mention the work of Das et al, who proposed to use such models for pattern classification [SRD16] and the work of Takada et al, who designed asynchronous self-reproducing loops [TIPM07a]. These are only some entry point to Figure 9: Rapid coalescence phenomenon for ECA 46 with fully asynchronous updating.…”

Asynchronous Cellular Automata

“…This framework is also analysed in detail by Dennunzio et al, who examined how the theory of measure can be applied to one-dimensional systems defined on an infinite line [DFMM13, DFM + 17]. As an example of a possible application of the use of these dynamical systems, we mention the work of Das et al, who proposed to use such models for pattern classification [SRD16] and the work of Takada et al, who designed asynchronous self-reproducing loops [TIPM07a]. These are only some entry point to the literature on this topic and we refer again to our survey paper for a wider scope [Fat14a].…”

Logic Gates Formed by Perturbations in an Asynchronous Game of Life

“…Specifically, the AGL is the normal GL with an asynchronous rate p async , a probability that the states of the cells will not be updated. There are many studies about such asynchronous cellular automata [7][8][9]. Furthermore, in this study, perturbations were introduced into the GL system by stochastically reversing the states of cells.…”