Descriptional complexity of cellular automata and decidability questions

We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata

Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow

Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method

A combined neuro fuzzy-cellular automata based material model for finite element simulation of plane strain compression

This paper presents a modelling strategy that combines Neuro-Fuzzy methods to define the material model with Cellular Automata representations of the microstructure, all embedded within a Finite Element solver that can deal with the large deformations of metal processing technology. We use the acronym nf-CAFE as a label for the method. The need for such an approach arises from the twin demands of computational speed for quick solutions for efficient material characterisation by incorporating metallurgical knowledge for material design models and subsequent process control. In this strategy, the cellular automata hold the microstructural features in terms of sub-grain size and dislocation density which are modelled by a neuro-fuzzy system that predicts the flow stress. The proposed methodology is validated on a two dimensional (2D) plane strain compression finite element simulation with Al-1% Mg alloy. Results from the simulations show the potential of the model for incorporating the effects of the underlying microstructure on the evolving flow stress fields. In doing this, the paper highlights the importance of understanding the local transition rules that affect the global behaviour during deformation