Automata Systems Research Articles

Parallel communicating Watson-Crick automata systems

Watson-Crick automata are finite state automata working on double-stranded tapes, introduced to investigate the potential of DNA molecules for computing. In this paper we introduce the concept of p...

Emergent behavior in two complex cellular automata rule sets: Research Articles

Cellular automata systems often produce complex behavior from simple rule sets. The behaviors and results of two complex combinations of cellular automata rules are analyzed. Both two-dimensional rule sets add complexities to typical cellular automata systems by attaching attributes and rules to each cell. One of the rule sets produces gliders that reproduce upon collision, whereas the other grows into an intricate shape. Projection and entropy analysis classify the rule sets as complex for the intricate shape, but measurements indicate that the self-reproducing gliders fall between ordered and complex classification, despite their complex appearance. © 2005 Wiley Periodicals, Inc. Complexity 10: 45–55, 2005

Emergent behavior in two complex cellular automata rule sets

Cellular automata systems often produce complex behavior from simple rule sets. The behaviors and results of two complex combinations of cellular automata rules are analyzed. Both two-dimensional rule sets add complexities to typical cellular automata systems by attaching attributes and rules to each cell. One of the rule sets produces gliders that reproduce upon collision, whereas the other grows into an intricate shape. Projection and entropy analysis classify the rule sets as complex for the intricate shape, but measurements indicate that the self-reproducing gliders fall between ordered and complex classification, despite their complex appearance. © 2005 Wiley Periodicals, Inc. Complexity 10: 45–55, 2005

Breath to breadth: Peter Sydenham's introduction to management of engineering design

Breath to breadth: Peter Sydenham's introduction to management of engineering design

Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running.

BackgroundMany arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level.MethodsWe have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG.ResultsWe demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given.ConclusionsQuantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described.

Magnetic cellular automata (MCA) systems

Single-domain nanomagnets could potentially be used as magnetic logic elements. In this paper, the performance of magnetic cellular automaton (MCA) systems is assessed. The three main types are described briefly and one is analysed in detail. A micromagnetic model which uses Monte Carlo/Metropolis updating is described and shown to be able to reproduce room temperature experimental results. It is subsequently used to investigate a range of MCA system parameters. Emphasis is placed on the potential behaviour of real systems (those which operate at room temperature and which possess fabrication defects). It is found that real adiabatically clocked magnetic systems are likely to operate significantly more slowly than the previously projected limits.

Dynamical behavior of a two-dimensional cellular automaton with signal processing

We study the effect of signal cooperation in a 2D cellular-automaton model of traffic flow in cities. Two-state signals, which permit vertical or horizontal passage of vehicles, are introduced to all cells of the automaton system. We simulate the dynamics of vehicles for different samples of signal arrangement. Phase transition occurs between freely moving and jamming phases for the samples. The critical densities for the transition vary as the arrangement is changed. We find a case having the multistage transition between them. The origin of the behavior is examined.

Verifying lossy channel systems has nonprimitive recursive complexity

Lossy channel systems are systems of finite state automata that communicate via unreliable unbounded fifo channels. It is known that reachability, termination and a few other verification problems are decidable for these systems. In this article we show that these problems cannot be solved in primitive recursive time.

Performance assessment of adiabatic quantum cellular automata

We investigate the feasibility of an adiabatic logic scheme for cellular automaton systems recently proposed by Tóth and Lent [J. Appl. Phys. 85, 2977 (1999)], based on structured arrays of six-dot cells and on the use of a four-phase trapezoidal clock. With respect to the original quantum cellular automaton (QCA) concept, focused on ground state computation, a clocked scheme would have the advantage of being immune to the presence of metastable states and would allow pipelined operation, at the expense of additional complexity, due to the clock distribution circuitry. Based on realistic cell geometries and material systems, we have evaluated the obtainable switching times of QCA cells, and have determined the region in the parameter space that allows operation at a reasonable clock speed.

PARALLEL COMMUNICATING PUSHDOWN AUTOMATA SYSTEMS

We consider automata systems consisting of several pushdown automata working in parallel and communicating the contents of their stacks by request, using a communication strategy borrowed from grammar system theory. We investigate the computational power of these mechanisms. We prove that non-centralized parallel communicating pushdown automata systems with a bounded number of components, where each automaton is allowed to issue a query, are able to recognize all recursively enumerable languages. We also present homomorphical characterizations of the class of recursively enumerable languages for the centralized variants, where only a distinguished automaton issues queries. Moreover, we show that these centralized variants are at least as powerful as one-way multihead pushdown automata. Finally, some open problems and further directions of research are discussed.

On complete systems of automata

A primitive product is a composition of a finite sequence of finite automata such that feedback is limited to no further than the previous factor. Furthermore, the input to each factor depends only on the global input to the system and the states of at most three factors (including the factor itself). Conversely, the state of a factor may directly influence only at most three factors (including the factor itself). Additional conditions guarantee a strong planarity property known as outerplanarity. Any primitive product of automata can be realized in an outerplanar layout. This is desirable from the engineering point of view of simple circuit wiring as a circuit whose components and wires comprise the nodes and edges of an outerplanar graph may be realized on a two-dimensional surface, and moreover, new wires can be run from a point outside the circuit to any or all nodes of the circuit without crossing each other or any existing wires. We constructively show that if A is a finite automaton satisfying Letichevsky's criterion, then any finite automaton can be homomorphically represented by (i.e. is a homomorphic image of a subautomaton of, or equivalently, is a letter-to-letter [length-preserving] divisor of) a primitive product of copies of A . A class K of finite automata is homomorphically complete under a given product π, by definition, if every finite automaton can be homomorphically represented as a π-product of automata from K . By Letichevsky's characterization of homomorphically complete classes under the general product (unrestricted finite composition), our results imply that a class of finite automata is homomorphically complete under the general product if and only if it is homomorphically complete under the primitive product.

On the equivalence of the cube-product and the general product of automata

In this work it is shown that the general product is equivalent to the cube-product with respect to the isomorphic representation. Using this equivalence we characterize the homomorphically complete systems of automata with respect to the cube-product. Furthermore, several earlier results and new results are concluded as consequences of this equivalence.

Learning automata algorithms for pattern classification

This paper considers the problem of learning optimal discriminant functions for pattern classification. The criterion of optimality is minimising the probability of misclassification. No knowledge of the statistics of the pattern classes is assumed and the given classified sample may be noisy. We present a comprehensive review of algorithms based on the model of cooperating systems of learning automata for this problem. Both finite action set automata and continuous action set automata models are considered. All algorithms presented have rigorous convergence proofs. We also present algorithms that converge to global optimum. Simulation results are presented to illustrate the effectiveness of these techniques based on learning automata.

On time reduction and simulation in cellular spaces

We prove a generalized and corrected version of the time reduction theorem for cellular spaces. One basic tool for investigations in this field is the concept of simulation between systems of automata. We propose a general formal definition of the intuitive concept and relate it to the notions which appear in the literature

A feedforward neural network behaving as a hierarchical system of automata

A new design principle of a feedforward neural network is presented. The built net behaves as a hierarchical system of automata where each action of an automaton at a certain level triggers an automaton at the level directly below it. The activation of hidden nodes is governed by the excitation degree of the input layer. The learning algorithm, based on the gradient search method, updates only the selected hidden node parameters. The studied network reduces the computational load in both training and operating steps. Simulation results show the effectiveness of the proposed network compared with the conventional feedforward neural network.

Application of a renormalization group algorithm to nonequilibrium cellular automata with one absorbing state

We improve a recently proposed dynamically driven renormalization group algorithm for cellular automata systems with one absorbing state, introducing spatial correlations in the expression for the transition probabilities. We implement the renormalization group scheme considering three different approximations which take into account correlations in the stationary probability distribution. The improved scheme is applied to a probabilistic cellular automaton already introduced in the literature.

A formal language model for parsing SGML

The Standard Generalized Markup Language (SGML) is an international standard for document definition (ISO 8879) that was adopted in 1986 and is rapidly gaining acceptance in industry and government. It is a meta-language system for document design rather than a specific scheme for document processing; almost any kind of document can be described using SGML. Productions called element declarations are used to define arbitrary elements of documents and the context in which they can occur. A finite set of element declarations called a document type definition (DTD) defines the high-level syntax of a set of documents. DTDs are similar to context-free grammars, but the productions are more complex. The standard does not describe a formal language model for SGML, and there is little work in the literature on this topic. This article defines a formal language model for SGML; systems of finite automata from systems of regular expressions. This model is applied in two ways: a parser is constructed for DTDs, and methods are shown for automatically constructing parsers for the documents defined by a DTD. These methods for parsing SGML are new, and they include features of DTDs that have not previously been included in a static language model. The model applies directly to the syntactic constructs of SGML, and thus, the methods shown in this article have distinct advantages for parsing SGML over traditional context-free parsing methods.

On the completeness of systems of finite automata

On the completeness of systems of finite automata

Chaos in cellular automaton systems with Toom rule

The critical behaviour of cellular automata can be studied like in chaotic systems as the sensitivity to initial conditions. We find the fractal dimension for the basin boundary set of the attracting configurations. Morever, obtained data allow us to qualify configurations from the attracting set.

Simulation of load balancing with cellular automata

In this paper the applicability and the speedup potential of a new load balancing strategy for distributed and parallel systems will be investigated by simulations. For this purpose, we will define a cellular automaton system which can produce process migration proposals according to the load states of computing nodes. The new strategy will be tested using our simulation environment CABLE. The simulation results for workstation clusters indicate that this new method possesses good applicability and a significant speedup.