General Cellular Automata Research Articles

Block approximations for probabilistic mixtures of elementary cellular automata

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied, making the study of their phase diagrams particularly interesting. The block approximation method, also known in this context as the local structure approach, is a powerful tool for studying the main features of these diagrams, improving upon Mean Field results. This work considers systems with multiple stationary states, aiming to understand how their interactions give rise to the structure of the phase diagram. Additionally, it shows how a simple algorithmic implementation of the block approximation allows for the effective study of the phase diagram even in the presence of several absorbing states.

A generalization of cellular automata over groups

Let G be a group and let A be a finite set with at least two elements. A cellular automaton (CA) over AG is a function defined via a finite memory set and a local function . The goal of this paper is to introduce the definition of a generalized cellular automaton (GCA) , where H is another arbitrary group, via a group homomorphism . Our definition preserves the essence of CA, as we prove analogous versions of three key results in the theory of CA: a generalized Curtis-Hedlund Theorem for GCA, a Theorem of Composition for GCA, and a Theorem of Invertibility for GCA. When G = H, we prove that the group of invertible GCA over AG is isomorphic to a semidirect product of and the group of invertible CA. Finally, we apply our results to study automorphisms of the monoid consisting of all CA over AG . In particular, we show that every defines an automorphism of via conjugation by the invertible GCA defined by , and that, when G is abelian, is embedded in the outer automorphism group of . Communicated by Pedro Garcia-Sanchez

Dynamics and Complexity of Computrons.

We investigate chaoticity and complexity of a binary general network automata of finite size with external input which we call a computron. As a generalization of cellular automata, computrons can have non-uniform cell rules, non-regular cell connectivity and an external input. We show that any finite-state machine can be represented as a computron and develop two novel set-theoretic concepts: (i) diversity space as a metric space that captures similarity of configurations on a given graph and (ii) basin complexity as a measure of complexity of partitions of the diversity space. We use these concepts to quantify chaoticity of computrons’ dynamics and the complexity of their basins of attraction. The theory is then extended into probabilistic machines where we define fuzzy basin partitioning of recurrent classes and introduce the concept of ergodic decomposition. A case study on 1D cyclic computron is provided with both deterministic and probabilistic versions.

Neighborhood-history quantum walk

History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of the walk. We generalize this model to the neighborhood-history quantum walk (NHQW), in which the walk dynamics and the state of the memory qubits in a neighborhood of the particle’s position are interdependent. To demonstrate it, we construct an NHQW on a one-dimensional lattice, with a simple neighborhood. Several dynamically interesting history dependent QWs can be realized as single-particle sectors of quantum lattice gas automata. In contrast, the NHQW constructed in this paper is realized as a single-particle sector of the more general quantum cellular automaton. The complexity of the NHQW dynamics presents a promising avenue toward richer walk strategies and a potentially useful model of QWs for the Noisy Intermediate-Scale Quantum era of quantum computing. It also modifies QWs to conceivably allow for modeling fundamental physics incorporating quantum field interactions with particles.

Swarm Networks in Brownian Environments

Swarm Networks are a generalization of Cellular Automata, in which the neighborhoods and functionalities of cells are determined by the presence or absence of connections between cells. This paper presents a Swarm Network in which connections can be changed dynamically, and in which the cells (called “agents”) are subject to Brownian motion. According to these characteristics, the model mimics behavior typically encountered in biological organisms. We show that this model is capable of universal computation by constructing a universal Brownian circuit based on it.

FPGA implementation of general cellular automata based cryptographic hash functions: performance and effectiveness

FPGA implementation of general cellular automata based cryptographic hash functions: performance and effectiveness

Research of Cellular Automata Model of Dockyard Ship Shifting Scheduling Problem and Its Ant Colony Algorithm

Abstract Shipyard ship shifting scheduling problem is a NP hard problem. By analyzing the characteristics of the problem, gradually present the general cellular automata model of the problem with the cellular automata theory, and explore the evolution rules of the CA model. Based on the evolution rules of the model, we proposal a general algorithm ideas and processes of the model. Finally, the Ant Colony Algorithm of the model is presented and the validity and convergence of the algorithm is proved. The topic of the paper is that provides an idea for shipyard shifting scheduling problem modeling.

A Dynamic Graph Automata Approach to Modeling Landscape Change in the Andes and the Amazon

A generalization of cellular automata was developed that allows flexible, dynamic updating of variable neighborhood relationships, which in turn allows the integration of interactions at widely disparate spatial and temporal scales. Cells in the landscapes were modeled as vertices of dynamic graph automata that allow temporally variable causal connectivity between spatially nonadjacent cells. A trial was carried out to represent changes in an Amazonian and a tropical Andean landscape modeled as dynamic graph automata with input from a Landsat TM-derived Level 1 classification with the following classes: for the Amazon—forest, nonforest vegetation, water, and urban or bare (soil); for the Andes—forest, scrub (shrub or grassland), agriculture, and bare or exposed ground. Explicit automata transition rules were used to simulate temporal land-cover change. These rules were derived independently from fieldwork in each area, including vegetation plots or transects and informal interviews. Such a generalization of cellular automata was useful for modeling land-use–land-cover change (LULCC), although it potentially increases the computational complexity of an already data intensive process (involving 5–8 million cells, in 1000 stochastic simulations, with each simulation encompassing 15 annual time steps). The interannual predicted LULCC, while more nuanced in the Andean site, poses a serious threat to compositional and configurational stability in both the Andes and the Amazon, with implications for landscape heterogeneity and habitat fragmentation.

A Programmable Hardware Cellular Automaton: Example of Data Flow Transformation

We present an IP-core called PHCA which stands for programmable hardware cellular automaton. PHCA is a hardware implementation of a general purpose cellular automaton (CA) entirely programmable. The heart of this structure is a PE array with reconfigurable side links allowing the implementation of a 2D CA or a 1D CA. As an illustration of a PHCA program, we present the implementation of a symmetric cryptography algorithm called ISEA for Ising spin encryption algorithm. Indeed ISEA is based on a 2D Ising spin lattice presenting random series of disordered spin configurations. The main idea of ISEA is to use this disorder to encrypt data. Efficiency of ISEA and PHCA implementation results are given.

A new stochastic cellular automaton model on traffic flow and its jamming phase transition

A general stochastic traffic cellular automaton (CA) model, which includes the slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well-known traffic CA models such as the Nagel?Schreckenberg model, the quick-start model and the slow-to-start model as specific cases. Fundamental diagrams of this new model clearly show metastable states around the critical density even when the stochastic effect is present. We also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow-density relations at boundaries. These phase transition curves are in excellent agreement with numerical results.

An evolving algebra approach to formal description of a class of automata networks

The Automata Networks considered here and called Hyperbolic Cellular Automata are based on Iterated Function Systems and can be considered as a generalization of Cellular Automata. The Evolving Algebras have been proposed by Yuri Gurevich to be the models for arbitrary computational processes. They provide a formal method for executable specifications. In the paper, an evolving algebra approach to formal description of Hyperbolic Cellular Automata is presented.

Modelling biological invasions: species traits, species interactions, and habitat heterogeneity

In this paper we explore the integration of different factors to understand, predict and control ecological invasions, through a general cellular automaton model especially developed. The model includes life history traits of several species in a modular structure interacting multiple cellular automata. We performed simulations using field values corresponding to the exotic Gleditsia triacanthos and native co-dominant trees in a montane area. Presence of G. triacanthos juvenile bank was a determinant condition for invasion success. Main parameters influencing invasion velocity were mean seed dispersal distance and minimum reproductive age. Seed production had a small influence on the invasion velocity. Velocities predicted by the model agreed well with estimations from field data. Values of population density predicted matched field values closely. The modular structure of the model, the explicit interaction between the invader and the native species, and the simplicity of parameters and transition rules are novel features of the model.

Parallel turing machines with one-head control units and cellular automata

Parallel Turing machines ( Ptm) can be viewed as a generalization of cellular automata ( Ca) where an additional measure called processor complexity can be defined which indicates the “amount of parallelism” used. In this paper Ptm are investigated with respect to their power as recognizers of formal languages. A combinatorial approach as well as diagonalization are used to obtain hierarchies of complexity classes for Ptm and Ca. In some cases it is possible to keep the space complexity of Ptm fixed. Thus for the first time it is possible to find hierarchies of complexity classes (though not Ca classes) which are completely contained in the class of languages recognizable by Ca with space complexity n and in polynomial time. A possible collapse of the time hierarchy for these Ca would therefore also imply some unexpected properties of Ptm.

A general cellular automaton model for surface reactions

A general cellular automaton model for surface reactions is introduced that shows almost quantitative agreement with the corresponding Monte Carlo simulations for several surface reaction models. It is generally applicable and can be easily extended to new surface reaction models. The high performance and the parallelism of cellular automaton simulations opens the possibility to investigate long simulation times and systems on large lattices.

On parallel Turing machines with multi-head control units

This paper deals with parallel Turing machines with multi-head control units on one or more tapes which can be considered as a generalization of cellular automata. We discuss the problem of finding an appropriate measure of space complexity. A definition is suggested which implies that the model is in the first machine class. It is shown that without loss of generality it suffices to consider only parallel Turing machines of certain normal forms.

An Incoherent Multiple-imaging System for Cellular Automata

Abstract An optical incoherent implementation of a general and programmable cellular automaton is reported. The implementation is based on an incoherent multiple-imaging system and electronic nonlinear circuits. All of 256 distinct local rules of a 1D elementary cellular automaton are achieved by simply specifying the different transparencies of a spatial light modulator (SLM) mask. The complex cellular automata can be synthesized based on the optical system. Simulations and experimental results are also given.

Completely deterministic self-organized critical state of sandpile automaton models

We study the general Abelian sandpile cellular automaton model of self-organized criticality in which the toppling conditions depend on the local height. We find that under some special kind of toppling rules, the self-organized critical states become completely deterministic, that is, the evolution of the system depends only on the total number of particles added to it but is totally independent of where you drop those particles. The results is quite general and can be applied to various models of self-organized criticality. The result has a close resemblance with the study of periodic behavior of circle maps in chaos.

The analysis of one-dimensional linear cellular automata and their aliasing properties

It is shown how to construct a general linear hybrid cellular automaton (CA) such that it has a maximum length cycle, and how the aliasing properties of such automata compare with linear feedback shift registers (LFSRs) when used as signature analyzers. The construction is accomplished by formally demonstrating the isomorphism which binds this kind of CA to the LFSRs. Consequently, these CAs can be analyzed as linear machines. Linear algebraic techniques are then applied appropriately for the transformations, and a useful search algorithm is developed which, given an irreducible characteristic polynomial, finds a corresponding linear hybrid automaton. Such CAs are tabulated for all irreducible and primitive polynomials up to degree 16, plus a selection of others of higher degree. The behavior of a linear hybrid CA and that of its corresponding LFSR are similar-that is, they have the same cycle structure and only relabel the states. The aliasing properties, when they are used as signature analyzers, remain unchanged.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Some applications of information theory to cellular automata

In this paper general deterministic one-dimensional cellular automata are identified with mappings of the unit interval into itself. This allows the machinery of dynamical systems analysis to be employed. The emphasis of the paper, however, is on applications of existing concepts and techniques of information theory to these automata. A basic paper by W.M. Conner is utilized to obtain equality of the capacity and Hausdorff dimension of each line of the automata, and existence of limiting values of these quantities is established. Assuming a probability measure on the initial line that is stationary and ergodic for the shift, a consistent ergodic theory is derived for any finite or infinite collection of lines of the automata. A body of related work by Russian authors on probabilistic automata is briefly examined. Important questions about the existence and properties of limiting distributions remain unresolved.

Parallel Image Processing by Memory-Augmented Cellular Automata

This paper introduces a generalization of cellular automata in which each celi is a tape-bounded Turing machine rather than a finite-state machine. Fast algorithms are given for performing various basic image processing tasks by such automata. It is suggested that this model of parallel computation is a very suitable one for studying the advantages of parallelism in this domain.