On the Properties of Language Classes Defined by Bounded Reaction Automata

Reaction automata are a formal model that has been introduced to investigate the computing powers of interactive behaviors of biochemical reactions([14]). Reaction automata are language acceptors with multiset rewriting mechanism whose basic frameworks are based on reaction systems introduced in [4]. In this paper we continue the investigation of reaction automata with a focus on the formal language theoretic properties of subclasses of reaction automata, called linearbounded reaction automata (LRAs) and exponentially-bounded reaction automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by lambda-LRAs) by allowing lambda-moves in the accepting process of reaction, and investigate the closure properties of language classes accepted by both LRAs and lambda-LRAs. Further, we establish new relationships of language classes accepted by LRAs and by ERAs with the Chomsky hierarchy. The main results include the following : (i) the class of languages accepted by lambda-LRAs forms an AFL with additional closure properties, (ii) any recursively enumerable language can be expressed as a homomorphic image of a language accepted by an LRA, (iii) the class of languages accepted by ERAs coincides with the class of context-sensitive languages.Comment: 23 pages with 3 figure

A simple model of the Belousov-Zhabotinsky reaction from first principles

The Belousov-Zhabotinsky (BZ) reaction is an example of a temporally oscillating chemical reaction. An unusual and interesting feature of the reaction is that as it progresses on a twodimensional plate, self-organized spirals are formed. Many computer models have been constructed of the BZ reaction to simulate the evolution of these spirals. The models typically use cellular automata to allow progression of a wavefront through a notional substrate. Usually a single substrate is used with somewhat arbitrary transference rules. Here it is shown that cellular automata models of BZ spirals can be created by using a very simple set of equations based on a three substrate model with close connection to reaction-diffusion models, more closely resembling the actual BZ reaction. Source code for the model is given in the Processing language

Reaction Automata

Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that feature (string) language acceptors with multiset manipulation as a computing mechanism, and show that reaction automata are computationally Turing universal. Further, some subclasses of reaction automata with space complexity are investigated and their language classes are compared to the ones in the Chomsky hierarchy.Comment: 19 pages, 6 figure

Evolving localizations in reaction-diffusion cellular automata

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules is required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.Comment: Accepted for publication in Int. J. Modern Physics

A New Class of Cellular Automata for Reaction-Diffusion Systems

We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion, and a probabilistic table-lookup for the reactive part. The applicability of the new CA is demonstrated using the Ginzburg-Landau equation.Comment: 4 pages, RevTeX 3.0 , 3 Figures 214972 bytes tar, compressed, uuencode

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

Reaction-diffusion fronts with inhomogeneous initial conditions

Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time-evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.Comment: 11 pages, 3 figures, submitted to J. Phys.