Showing papers on "Continuous automaton published in 2003"

Euler-lagrange correspondence of cellular automaton for traffic-flow models.

Abstract: We propose a Euler-Lagrange transformation for cellular automata (CA) by developing new explicit transformation formulas. This transformation is done in the fully discrete level of variables, and corresponds to the well-known continuous version of it which appears in continuous mechanics such as fluid dynamics and plasma physics. Applying this method to the traffic problem, we have obtained the Lagrange representation of a traffic model, and also succeeded in clarifying the relation between different types of traffic models. It is shown that the Burgers CA, which is a corresponding CA of the continuous Burgers equation, plays a central role in considering this relation.

Cellular automata with vanishing particles

Abstract: We consider particle weight functions which assign weights to certain words. Given a cellular automaton, we search for particle weight functions, for which the total weights of configurations do not increase with time. In this case the weight of a shift-invariant Borel probability measure does not increase either, so we get a Ljapunov function on the space of measures. We give some conditions which ensure that the weight of a measure converges to zero. In particular we prove that this happens in the elementary cellular automaton rule number 18 and in a variant of the Gacs-Kurdyumov-Levin cellular automaton.

Real-time generation of primes by a 1-bit-communication cellular automaton

Abstract: It is shown that an infinite prime sequence can be generated in real-time by a cellular automaton having 1-bit inter-cell communications (CA_{1-bit}). The algorithm presented is based on the classical sieve of Eratosthenes, and its implementation will be made on a CA_{1-bit} using 34 internal states and 71 transition rules.

Cellular automata and intermediate degrees

Abstract: We study a classification of cellular automata based on the Turing degree of the orbits of the automaton. The difficulty of determining the membership of a cellular automaton in any one of these classes is characterized in the arithmetical hierarchy.

Coinductive counting with weighted automata

Abstract: A general methodology is developed to compute the solution of a wide variety of basic counting problems in a uniform way: (1) the objects to be counted are enumerated by means of an infinite weighted automaton; (2) the automaton is reduced by means of the quantitative notion of stream bisimulation; (3) the reduced automaton is used to compute an expression (in terms of stream constants and operators) that represents the stream of all counts.

Efficient Cellular Automata for 2D / 3D Free-Form Modeling

Abstract: This paper presents an approach for efficiently simulating highly deformable 2D substances undergoing viscoplastic deformations in real time. The user deals with objects in the same way as clay works. Based on the work of Y. Takai and H. Arata, we suggest a new approach for the computation of repartition rules. We use a discrete 2D space in which each pixel is given a certain amount of clay at the intialisation of the system. The user’s tool only moves some clay from a pixel to another, creating an overload. The repartition of this overload amoung the neighbours is then made according to the laws of plastic deformation thanks to a cellular automaton.

Research of complex forms in cellular automata by evolutionary algorithms

Abstract: This paper presents an evolutionary approach for the search for new complex cellular automata. Two evolutionary algorithms are used: the first one discovers rules supporting gliders and periodic patterns, and the second one discovers glider guns in cellular automata. An automaton allowing us to simulate AND and NOT gates is discovered. The results are a step toward the general simulation of Boolean circuits by this automaton and show that the evolutionary approach is a promising technic for searching for cellular automata that support universal computation.

Syntactic semiring and universal automaton

Abstract: We discuss the relationships between the minimal automaton, the universal automaton, the syntactic monoid and the syntactic semiring of a given regular language We use certain completions and reductions of the transformation matrix of the minimal automaton to clarify those connections

Syntactic semiring and universal automaton

Abstract: We discuss the relationships between the minimal automaton, the universal automaton, the syntactic monoid and the syntactic semiring of a given regular language. We use certain completions and reductions of the transformation matrix of the minimal automaton to clarify those connections.

Almost periodic configurations on linear cellular automata

Abstract: We study computational properties of linear cellular automata on configurations that differ from spatially periodic ones in only finitely many places. It is shown that the degree structure of the orbits of cellular automata is the same on these configurations as on the space of finite configurations. We also show that it is undecidable whether the cellular automaton exhibits complicated behavior on configurations of sufficiently long spatial periods and exhibit cellular automata with undecidable orbits whose orbits on backgrounds of all fixed sizes are decidable.

A first approach for a possible cellular automaton model of fluids dynamics

Abstract: In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the evolution in time for a two-dimensional grid, where one molecule of the material fluid can ideally place itself on a single geometric square. By mean of computational simulations, some realistic effects, here showed by use of digital pictures, have been obtained. In a subsequent step of this work I think to use a parallel program for a high performances computational simulation, for increasing the degree of realism of the digital rendering by mean of a three-dimensional grid too. For the execution of the simulations, numerical methods of resolution for differential equations have not been used.

Bideterministic automata and minimal representations of regular languages

Abstract: Bideterministic automata are deterministic automata with the property of their reversal automata also being deterministic. It has been known that a bideterministic automaton is the minimal deterministic automaton accepting its language. This paper shows that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language. We also present a more general result that shows that under certain conditions a minimal deterministic automaton accepting some language or the reversal of the minimal deterministic automaton of the reversal language is a minimal automaton representation of the language. These conditions can be checked in polynomial time.

On one-way cellular automata with a fixed number of cells

Abstract: We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA.

Data and signals: a new kind of cellular automaton for growing systems

Abstract: Traditionally the cell of an automaton implements the rule table defining the state of the cell at the next time step knowing its present state and those of its neighbors. The cell consequently processes only with states. The novel cell presented here handles data and signals. It is designed as a digital system made up of a processing unit and a control unit. The realization of interactive self-replicating loops will serve as an application example of growing systems. The hardware implementation of these loops takes place in our electronic wall for bio-inspired applications, the BioWall.

Extensions in reversible one-dimensional cellular automata are equivalent with the full shift

Abstract: Cellular automata are discrete dynamical systems based on simple local interactions among its components, but sometimes they are able to yield quite a complex global behavior. A special kind of cellular automaton is the one where the global behavior is invertible, this type of cellular automaton is called reversible. In this paper we expose the graph representation provided by de Bruijn diagrams of reversible one-dimensional cellular automata and we define the distinct types of paths between self-loops in such diagrams. With this, we establish the way in which a reversible one-dimensional cellular automaton generates sequences composed by subsequences produced by the undefined repetition of a single state. Using this graph presentation, we define Welch diagrams which will be useful for proving that all the extensions of the ancestors in reversible one-dimensional cellular automata are equivalent to the full shift. In this way an important result of this paper is that we understand and classify the behavior of a reversible automaton analyzing the extensions of the ancestors of a given sequence by means of symbolic dynamics tools. A final example illustrates the results exposed in the paper.

On transition rules of complex structures in one-dimensional cellular automata: Some implicaltions for urban change

Abstract: Based on the assumptions that cities are semi-lattices and that their spatial configuration are complex structure, I use one-dimensional cellular automaton representing a hypothetical, linear city as an analytic tool to investigate possible transition rules fulfilling these requirements, and base on that metaphor to draw some implications for urban change. For two-value (k=2), one-neighbor (r=1) one-dimensional cellular automata, the stochastic transition rules thus found imply that determinism at one level can give rise to stochasticity at another level, and that the seemingly stochastic processes of urban change might indeed be governed by a few deterministic transition rules.

Spectral properties of reversible one-dimensional cellular automata

Abstract: Reversible cellular automata are invertible dynamical systems characterized by discreteness, determinism and local interaction This article studies the local behavior of reversible one-dimensional cellular automata by means of the spectral properties of their connectivity matrices We use the transformation of every one-dimensional cellular automaton to another of neighborhood size 2 to generalize the results exposed in this paper In particular we prove that the connectivity matrices have a single positive eigenvalue equal to 1; based on this result we also prove the idempotent behavior of these matrices The significance of this property lies in the implementation of a matrix technique for detecting whether a one-dimensional cellular automaton is reversible or not In particular, we present a procedure using the eigenvectors of these matrices to find the inverse rule of a given reversible one-dimensional cellular automaton Finally illustrative examples are provided

From regular weighted expressions to finite automata

Abstract: In this article we generalize the concepts of position automaton and ZPC structure to the regular K-expressions. We show that the ZPC structure can be built in linear time in the size of the expression and that the associated position automaton can be deduced from it in quadratic time.

Systems and methods for determining the N-best strings of an automaton

Abstract: Systems and methods for identifying the N-best strings of a weighted automaton. A potential for each state of an input automaton to a set of destination states of the input automaton is first determined. Then, the N-best paths are found in the result of an on-the-fly determinization of the input automaton. Only the portion of the input automaton needed to identify the N-best paths is determinized. As the input automaton is determinized, a potential for each new state of the partially determinized automaton is determined and is used in identifying the N-best paths of the determinized automaton, which correspond exactly to the N-best strings of the input automaton.

Symmetric Self-Organization in a Cellular Automaton Requiring AN Essentially Random Feedback: Observations, Conjectures, Questions

Abstract: A triangular cellular array whose cell-states satisfy the local rule of the cellular automaton that generates Pascal's triangle modulo 2 is subjected to a feedback inspired by conditions for rotational symmetry of its state-pattern. We discuss observations and conjectures about the fact that, in order to stabilize effectively in a rotationally symmetric pattern, the underlying recursion (feedback) procedure must have an essentially random nature.

Reversible one-dimensional cellular automata with one of the two Welch indices equal to 1 and full shifts

Abstract: Reversible cellular automata are invertible discrete dynamical systems which have been widely studied both for analysing interesting theoretical questions and for obtaining relevant practical applications, for instance, simulating invertible natural systems or implementing data coding devices. An important problem in the theory of reversible automata is to know how the local behaviour which is not invertible is able to yield a reversible global one. In this sense, symbolic dynamics plays an important role for obtaining an adequate representation of a reversible cellular automaton. In this paper we prove the equivalence between a reversible automaton where the ancestors only differ at one side (technically with one of the two Welch indices equal to 1) and a full shift. We represent any reversible automaton by a de Bruijn diagram, and we characterize the way in which the diagram produces an evolution formed by undefined repetitions of two states. By means of amalgamations, we prove that there is always a way of transforming a de Bruijn diagram into the full shift. Finally, we provide an example illustrating the previous results.

Mathematical modelling and simulation of interacting cell systems with cellular automata

Abstract: Publisher Summary This chapter describes the cellular automaton model applications for bacterial pattern formation and avascular tumor growth. Principles underlying the dynamics of interacting cell systems can be analyzed by means of mathematical models. Cellular automata are discrete dynamical systems and provide a cell-based modelling alternative, in which the fate of individual cells can be tracked. Automaton configurations are updated synchronously or asynchronously, and they depend only on the local neighborhood configuration. The essential question is how macroscopic behavior can arise from individual rules. Cellular automata have become paradigms of self-organizing complex systems, in which collective behavior arises from simple interaction rules of even more simple components. An important insight of complex system research is that macroscopic behavior is rather independent of the precise choice of the microscopic interaction. Finally, the models introduced for the case of bacterial and tumor pattern formation can easily be adapted to gain theoretical insight into the behavior of a wide range of other biological systems.

Land Use Dynamics: a Cellular Automata

Abstract: Usually applications of urban growth cellular automata are related to an only one town, with transition rules and constraints a priori defined. This seems to be a severe limits in applications. The paper presented is born to follow a different kind of approach, so to have rules and constraints directly from observed past data. We consider ten European towns and for each one we have data for time series approx. 40 years long. We deduce rules and constraints directly from the data set, solving an inverse problem (in which we have input and output measures and we have to determine a system model).The study aims to define in detail the stochastic or deterministic character of transition rules (in the stochastic case evaluating transition probability). At last the rules are applied to towns maps (by means of ad hoc cellular automaton). With this cellular automaton we try to simulate past dynamics (for a validation of the model) and also to forecast the spatial development of the towns by means of scenarios (based on the past histories of the cities).

Automaton Modeling of Processes of Formation and Splitting of Collectives

Abstract: The problem of determination of the conditions of formation and splitting of a collective (a team) and the problem of determination of the response of a dynamic automaton to specified input processes are shown to be equivalent. Based on this fact, an automaton model of a collective is constructed. The apparatus of continuous logic and logical determinants are used to analyze the model.

Reduced power automata and sofic systems

Abstract: The state complexity of the cover language of sofic shifts arising from cellular automata is studied. It is shown that in the case where the underlying automaton is nearly a permutation automaton the deterministic automaton obtained by the classical Rabin-Scott construction is already reduced.