Asynchronous cellular learning automata

Cellular learning automata is a combination of cellular automata and learning automata. The synchronous version of cellular learning automata in which all learning automata in different cells are activated synchronously, has found many applications. In some applications a type of cellular learning automata in which learning automata in different cells are activated asynchronously (asynchronous cellular learning automata) is needed. In this paper, we introduce asynchronous cellular learning automata and study its steady state behavior. Then an application of this new model to cellular networks has been presented.     

Sand automata as cellular automata

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with simple sand automata. We show that the classical definition of nilpotency is not meaningful for sand automata. Then, we introduce the suitable new notion of flattening sand automata. Finally, we prove that this simple dynamical behavior is undecidable.     

Alternation on cellular automata

In this paper we consider several notions of alternation in cellular automata: non-uniform, uniform and weak alternation. We study relations among these notions and with alternating Turing machines. It is proved that the languages accepted in polynomial time by alternating Turing machines are those accepted by alternating cellular automata in polynomial time for all the proposed alternating cellular automata. In particular, this is true for the weak model where the difference between existential and universal states is omitted for all the cells except the first one. It is proved that real time alternation in cellular automata is strictly more powerful than real time alternation in Turing machines, with only one read-write tape. Moreover, it is shown that in linear time uniform and weak models agree.     

Traced communication complexity of cellular automata

We study cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by communicating as little as possible between each other. We present some links with classical dynamical concepts, especially equicontinuity, expansivity, entropy and give the asymptotic communication complexity of most elementary cellular automata.     

Bulking II: Classifications of cellular automata

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc.) providing several formal tools allowing to classify cellular automata.     

Effects of cell size and configuration in cellular automata based prey–predator modelling

Cellular automata (CA) have shown to be a viable approach in ecological modelling, in particular when dealing with local interactions between species and their environment. In CA modelling complex patterns emerge on a global scale through the evolution of interactions at a local level. Although the validity of a cell-based approach has successfully been demonstrated in numerous cases, very few studies have been reported that address the effects of cell size and configuration on the behaviours of CA-based models. In this paper, the performance of a cellular automaton based prey–predator model (EcoCA) developed by the author was first calibrated against the classical Lotka–Volterra (LV) model. The model was then used to investigate effects of cell size and cellular configurations (viz. the ‘computational stencil’). By setting up systematic simulation scenarios it was observed that the choice of a particular cell size has a clear effect on the resulting spatial patterns, while different cellular configurations affect both spatial patterns and system stability. On the basis of these findings, it is proposed to use the principal spatial scale of the studied ecosystem as CA model cell size and to apply the Moore type cell configuration. Methods for identifying principal spatial scales have been developed and are presented here.     

Hyperspectral image segmentation through evolved cellular automata

Segmenting multidimensional images, in particular hyperspectral images, is still an open subject. Two are the most important issues in this field. On one hand, most methods do not preserve the multidimensional character of the signals throughout the segmentation process. They usually perform an early projection of the hyperspectral information to a two dimensional representation with the consequent loss of the large amount of spectral information these images provide. On the other hand, there is usually very little and dubious ground truth available, making it very hard to train and tune appropriate segmentation and classification strategies. This paper describes an approach to the problem of segmenting and classifying regions in multidimensional images that performs a joint two-step process. The first step is based on the application of cellular automata (CA) and their emergent behavior over the hyperspectral cube in order to produce homogeneous regions. The second step employs a more traditional SVM in order to provide labels for these regions to classify them. The use of cellular automata for segmentation in hyperspectral images is not new, but most approaches to this problem involve hand designing the rules for the automata and, in general, average out the spectral information present. The main contribution of this paper is the study of the application of evolutionary methods to produce the CA rule sets that result in the best possible segmentation properties under different circumstances without resorting to any form of projection until the information is presented to the user. In addition, we show that the evolution process we propose to obtain the rules can be carried out over RGB images and then the resulting automata can be used to process multidimensional hyperspectral images successfully, thus avoiding the problem of lack of appropriately labeled ground truth images. The procedure has been tested over synthetic and real hyperspectral images and the results are very competitive.     

Directional dynamics along arbitrary curves in cellular automata

This paper studies directional dynamics on one-dimensional cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behavior of a cellular automaton through the conjoint action of its global rule (temporal action) and the shift map (spacial action): qualitative behaviors inherited from topological dynamics (equicontinuity, sensitivity, expansivity) are thus considered along arbitrary curves in space-time. The main contributions of the paper concern equicontinuous dynamics which can be connected to the notion of consequences of a word. We show that there is a cellular automaton with an equicontinuous dynamics along a parabola, but which is sensitive along any linear direction. We also show that real numbers that occur as the slope of a limit linear direction with equicontinuous dynamics in some cellular automaton are exactly the computably enumerable numbers.     

On cellular automata over Galois rings

In this paper we study the invertibility of one-dimensional cellular automata, determined by a local rule, acting on the space of all doubly-infinite sequences taking values in a finite Galois ring. We also compute the topological entropy of one-dimensional CA generated by additive local rule over a finite Galois ring. We conclude by showing that the topological entropy of an additive invertible CA over a finite Galois ring is equal to its inverse.     

Directional dynamics for cellular automata: A sensitivity to initial condition approach

A cellular automaton is a continuous function F defined on a full-shift which commutes with the shift σ. Often, to study the dynamics of F one only considers implicitly σ. However, it is possible to emphasize the spatio-temporal structure produced by considering the dynamics of the -action induced by (σ,F).In this purpose we study the notion of directional dynamics. In particular, we are interested in directions of equicontinuity and expansivity, which generalize the concepts introduced by Gilman [Robert H. Gilman, Classes of linear automata, Ergodic Theory Dynam. Systems 7 (1) (1987) 105–118] and P. Kůrka [Petr Kůrka, Languages, equicontinuity and attractors in cellular automata, Ergodic Theory Dynam. Systems 17 (2) (1997) 417–433]. We study the sets of directions which exhibit this special kind of dynamics showing that they induce a discrete geometry in space-time diagrams.     

A cellular automata model considering diversity associated with HIV infection

The diversity of human immunodeficiency virus (HIV) in vivo has been reported. In this article, we propose a cellular automata (CA) model describing the interactions between the immune system and HIV, and examine the effect of the diversity of these interactions. The novel aspects of our CA model are that it not only considers four states (HIV, virgin, dead, infect) but also the diversity exhibited by both HIV and T cells. We simulated maximum diversities for these states by simulating CA on a computer. The model revealed that increased diversity had the effect of increasing the HIV population and simulation steps. In addition, we observed that the CA model accurately reflects the occurrence of infection, incubation period, and the development of AIDS. The CA model demonstrated that the diversity of the virus is the major factor affecting the success rate of the escape of HIV from the immune response. This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, Oita, Japan, February 4–6, 2005     

Cryptanalysis of an involutional block cipher using cellular automata

In 2006, an involutional block cipher using cellular automata was proposed. A self-invertible CA-based structure allows for an efficient hardware implementation. This paper analyzes the insecurity of the cipher due to its conjugate property. The results of this study will make it possible to construct a decryption process without knowledge of the secret key.     

The Garden of Eden theorem for cellular automata on group sets

ABSTRACT

We prove the Garden of Eden theorem for big-cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It states that the global transition function of such an automaton is surjective if and only if it is pre-injective. Pre-Injectivity means that two global configurations that differ at most on a finite subset and have the same image under the global transition function must be identical. The theorem is proven by showing that the global transition function of an automaton as above is surjective if and only if its image has maximal entropy and that its image has maximal entropy if and only if it is pre-injective. Entropy of a subset of global configurations measures the asymptotic growth rate of the number of finite patterns with growing domains that occur in the subset.     

On behavior of two-dimensional cellular automata with an exceptional rule

Several studies [A.R. Khan, P.P. Choudhury, K. Dihidar, S. Mitra, P. Sarkar, VLSI architecture of a cellular automata, Comput. Math. Appl. 33 (1997) 79-94; A.R. Khan, P.P. Choudhury, K. Dihidar, R. Verma, Text compression using two-dimensional cellular automata, Comput. Math. Appl. 37 (1999) 115-127; K. Dihidar, P.P. Choudhury, Matrix algebraic formulae concerning some exceptional rules of two-dimensional cellular automata, Inf. Sci. 165 (2004) 91-101] have explored a new rule convention for two-dimensional (2-D) nearest neighborhood linear cellular automata (CA) with null and periodic boundary conditions. A variety of applications of the rule convention have been illustrated, and the VLSI architecture of cellular automata machine (CAM) has been proposed. However, most of the studies address the issue of the kernel dimension of 2-D CA, and many other important characteristics of CA, such as Garden of Eden (GOE), maximal transient length, maximal cycle length, etc., have not been explored. In this paper, by exploiting matrix algebra in GF(2) (the Galois field with two elements), we attempt to characterize the behavior of a specific rule, which is not covered in existing work but accords with the same convention. A necessary and sufficient condition is given to ensure that a given configuration is a GOE. Meanwhile, we propose some algorithms to determine the number of GOEs, the maximal transient length, and the maximal cycle length in a 2-D CA.     

Garden of eden configurations for 2-D cellular automata with rule 2460 N

An important problem in cellular automata theory is the reversibility of a cellular automaton which is related to the existence of Garden of Eden configurations in cellular automata. In this paper, we study new local rules for two-dimensional cellular automata over the ternary field Z₃ (the set of integers modulo three) with some of their important characteristics. We obtain necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional ternary cellular automata. Also by making use of the matrix representation of two-dimensional cellular automata, we provide an algorithm to obtain the number of Garden of Eden configurations for two-dimensional cellular automata defined by rule 2460 N. We present an application of the reversible two-dimensional ternary cellular automata to cryptography.     

Constructible functions in cellular automata and their applications to hierarchy results

We investigate time-constructible functions in one-dimensional cellular automata (CA). It is shown that (i) if a function t(n) is computable by an O(t(n)−n)-time Turing machine, then t(n) is time constructible by CA and (ii) if two functions are time constructible by CA, then the sum, product, and exponential functions of them are time constructible by CA. As an application, it is shown that if t₁(n) and t₂(n) are time constructible functions such that lim_n→∞ t₁(n)/t₂(n) = 0 and t₁(n)n, then there is a language which can be recognized by a CA in t₂(n) time but not by any CA in t₁(n) time.     

A new fast cellular automata orthogonal least-squares identification method

A novel fast cellular automata orthogonal least squares (FCA-OLS) identification method is introduced by extending and developing the CA-OLS identification method presented in a previous study by Billings and Yang. Both one-dimensional CA and two-dimensional CA were identified with FCA-OLS as the simulation examples. The simulation results show that the new method significantly reduces the computational time compared with existing methods.