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Showing papers on "Continuous automaton published in 2004"


Journal ArticleDOI
TL;DR: This paper implements three primitive operators on the cellular automaton from which any arbitrary delay-insensitive circuit can be constructed and shows how to connect the operators such that collisions of crossing signals are avoided.
Abstract: A known method to compute on an asynchronously updating cellular automaton is the simulation of a synchronous computing model on it. Such a scheme requires not only an increased number of cell states, but also the simulation of a global synchronization mechanism. Asynchronous systems tend to use synchronization only on a local scale—if they use it at all. Research on cellular automata that are truly asynchronous has been limited mostly to trivial phenomena, leaving issues such as computation unexplored. This paper presents an asynchronously updating cellular automaton that conducts computation without relying on a simulated global synchronization mechanism. The two-dimensional cellular automaton employs a Moore neighborhood and 85 totalistic transition rules describing the asynchronous interactions between the cells. Despite the probabilistic nature of asynchronous updating, the outcome of the dynamics is deterministic. This is achieved by simulating delay-insensitive circuits on it, a type of asynchronous circuit that is known for its robustness to variations in the timing of signals. We implement three primitive operators on the cellular automaton from which any arbitrary delay-insensitive circuit can be constructed and show how to connect the operators such that collisions of crossing signals are avoided.

67 citations


Proceedings Article
01 Jan 2004
TL;DR: The approach is evaluated in simulation and it is found that the self-reconfiguration process always converges and the time to complete a configuration scales approximately linearly with the number of modules.
Abstract: Self-reconfigurable robots are built from modules, which are autonomously able to change the way they are connected. Such a robot can, through this self-reconfiguration process, change its shape. The process has proven to be difficult to control, because it involves control of a distributed system of mechanically coupled modules connected in time-varying ways. In this paper we present an approach to the self-reconfiguration problem where the desired configuration is grown from an initial seed module. Seeds produce growth by creating a gradient in the system, using local communication, which spare modules climb to locate the seed. The growth is guided by a cellular automaton, which is automatically generated based on a three-dimensional CAD model or a mathematical description of the desired configuration. The approach is evaluated in simulation and we find that the self-reconfiguration process always converges and the time to complete a configuration scales approximately linearly with the number of modules. However, an open question is how the simulation results transfer to a physically realized self-reconfigurable robot.

52 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that there exist exactly 16 reversible elementary cellular automata rules for infinitely many cell sizes by means of a correspondence between elementary automata and the de Bruijn graph.
Abstract: Reversibility of one-dimensional cellular automata with periodic boundary conditions is discussed. It is shown that there exist exactly 16 reversible elementary cellular automaton rules for infinitely many cell sizes by means of a correspondence between elementary cellular automaton and the de Bruijn graph. In addition, a sufficient condition for reversibility of three-valued and two-neighbour cellular automaton is given.

32 citations


Journal ArticleDOI
TL;DR: A search technique using genetic algorithm is proposed, and it successfully find a few types of pattern spontaneously, that is, without giving a priori information on the type of pattern, and is expected to be applied to a wide range of potential studies related to self-organization.
Abstract: This paper proposes a class of two-dimensional asynchronous cellular automata with conservation of mass, for the formation of patterns in groups, and describes the merits given by this methodology. A cellular automaton rule causing a specified kind of pattern was designed manually. Thanks to this realistic modeling method reflecting nature, the mechanism of pattern formation was found to be similar to real chemical processes. Because of the conservation of mass, some “boring” cellular automata which evolve, for instance, into homogeneity are automatically excluded in this scheme. This is greatly advantageous for searching, automatically, for pattern-forming cellular automata. A search technique using genetic algorithm is proposed, and it successfully find a few types of pattern spontaneously, that is, without giving a priori information on the type of pattern. This technique is expected to be applied to a wide range of potential studies related to self-organization.

28 citations


Book ChapterDOI
26 Jun 2004
TL;DR: This papers provides elements of answer, as it describes how another universal cellular automaton than the Game of Life (Life) was sought and found using evolutionary algorithms.
Abstract: In Twenty Problems in the Theory of Cellular Automata, Stephen Wolfram asks “how common computational universality and undecidability [are] in cellular automata.” This papers provides elements of answer, as it describes how another universal cellular automaton than the Game of Life (Life) was sought and found using evolutionary algorithms. This paper includes a demonstration that consists in showing that the presented R automaton can both implement any logic circuit (logic universality) and a simulation of Life (universality in the Turing sense).

26 citations


Journal ArticleDOI
TL;DR: A novel CA where the cell handles data and signals is presented, designed as a digital system comprising a processing unit and a control unit that allows the realization of various growing structures, including self-replicating loops and biomorphs.
Abstract: In a traditional cellular automaton (CA) a cell is implemented by a rule table defining its state at the next time step, given its present state and those of its neighbors. The cell thus deals only with states. We present a novel CA where the cell handles data and signals. The cell is designed as a digital system comprising a processing unit and a control unit. This allows the realization of various growing structures, including self-replicating loops and biomorphs. We also describe the hardware implementation of these structures within our electronic wall for bio-inspired applications, the BioWall.

23 citations


Book ChapterDOI
01 Jan 2004

20 citations


Journal ArticleDOI
TL;DR: It is shown that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.
Abstract: In this article we generalize concepts of the position automaton and ZPC-structure to the regular -expressions. We show that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.

19 citations


Journal ArticleDOI
TL;DR: A quadratic upper bound for the neighborhood size of the inverse automaton of some types of one-dimensional reversible cellular automata is given, and it is shown that this bound can be lowered in some particular cases.

17 citations


Journal ArticleDOI
TL;DR: This work considers the finite homogeneous Markov chain induced by a class of one-dimensional asynchronous cellular automata—automata that are allowed to change only one cell per iteration, and shows that if the local transition rule is exponential, the stationary probability is the Boltzmann distribution of the Ising model.
Abstract: We consider the finite homogeneous Markov chain induced by a class of one-dimensional asynchronous cellular automata—automata that are allowed to change only one cell per iteration. Furthermore, we confine to totalistic automata, where transitions depend only on the number of 1s in the neighborhood of the current cell. We consider three different cases: (i) size of neighborhood equals length of the automaton; (ii) size of neighborhood two, length of automaton arbitrary; and (iii) size of neighborhood three, length of automaton arbitrary. For each case, the associated Markov chain proves to be ergodic. We derive simple-form stationary distributions, in case (i) by lumping states with respect to the number of 1s in the automaton, and in cases (ii) and (iii) by considering the number of 0–1 borders within the automaton configuration. For the three-neighborhood automaton, we analyze also the Markov chain at the boundary of the parameter domain, and the symmetry of the entropy. Finally, we show that if the local transition rule is exponential, the stationary probability is the Boltzmann distribution of the Ising model.

13 citations


Journal ArticleDOI
TL;DR: Here it is shown how to construct, for any second-order cellular automaton, a lattice gas having isomorphic functional behavior, and a trade-off between two ways of achieving a "force" of a given range.

Journal ArticleDOI
TL;DR: In this article, a conserved quantity for a reversible cellular automaton derived from a discrete-time quantum walk in one dimension was obtained, and detailed information regarding the evolution of the quantum walk was given.

Journal Article
TL;DR: In this article, the authors investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton using Antimirov's derived term of an expression.
Abstract: In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. If an automaton is then sufficiently decorated, the combination of these two algorithms gives the desired result. Reducing the amount of decoration is still the object of ongoing investigation.

Book ChapterDOI
22 Jul 2004
TL;DR: The design of an algorithm for computing the follow automaton via this structure makes it easier to compare all these small recognizers, and provides a straightforward alternative to the rather sophisticated handling of e-transitions used in the original algorithm.
Abstract: Small nondeterministic recognizers are very useful in practical applications based on regular expression searching. The follow automaton, recently introduced by Ilie and Yu, is such a small recognizer, since it is a quotient of the position automaton. The aim of this paper is to present an efficient computation of this quotient, based on specific properties of the $\mathcal{ZPC}$ of the expression. The motivation is twofold. Since this structure is already a basic tool for computing the position automaton, Antimirov’s automaton and Hromkovic’s automaton, the design of an algorithm for computing the follow automaton via this structure makes it easier to compare all these small recognizers. Secondly such an algorithm provides a straightforward alternative to the rather sophisticated handling of e-transitions used in the original algorithm.

Journal ArticleDOI
TL;DR: This work presents a procedure to calculate the ancestors for a given sequence of states, which is based on a special kind of graph called subset diagram, that is able to yield ancestors in several generations.
Abstract: One-dimensional cellular automata are dynamical systems characterized by discreteness (in space and time), determinism and local interaction. We present a procedure to calculate the ancestors for a given sequence of states, which is based on a special kind of graph called subset diagram. We use this diagram to specify subset tables for calculating ancestors which are not Garden-of-Eden sequences, hence the process is able to yield ancestors in several generations. Some examples are illustrated using the cellular automaton Rule 110 which is the most interesting automaton of two states and three neighbors.

Book ChapterDOI
05 Apr 2004
TL;DR: This paper investigates how it is possible to recover an automaton from a rational expression that has been computed from that automaton, and the notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem.
Abstract: In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. If an automaton is then sufficiently “decorated”, the combination of these two algorithms gives the desired result. Reducing the amount of “decoration” is still the object of ongoing investigation.

Book ChapterDOI
25 Oct 2004
TL;DR: This paper proposes a universal constructor on a self-timed cellular automaton (STCA), a particular type of ACA, in which cells are divided in four partitions, each with four states.
Abstract: Computation- and construction-universality in cellular automata (CA), first studied by von Neumann, has attracted steady research efforts, over the years, most employing synchronous CA. Asynchronous cellular automata (ACA), though of interest as most interactions in nature are asynchronous, have not been used for this task, other than by the indirect way of simulating a synchronous CA. In this paper, we propose a universal constructor on a self-timed cellular automaton (STCA), a particular type of ACA, in which cells are divided in four partitions, each with four states.

Book ChapterDOI
21 Sep 2004
TL;DR: This work describes the language related to a full transitive subshift extending the notion of irreducibility and shows how to associate to any subshift of finite type a cellular automaton which contains it.
Abstract: We study the subshift behavior of one dimensional cellular automata and we show how to associate to any subshift of finite type a cellular automaton which contains it. The relationships between some topological properties of subshifts and the behavior of the related languages are investigated. In particular we focus our attention to the notion of full transitivity. We characterize the language related to a full transitive subshift extending the notion of irreducibility.

Journal ArticleDOI
TL;DR: Two parallel substitution algorithms for modeling the self-reproduction of a cellular structure having the shape of a rectangular loop are presented.
Abstract: The parallel substitution algorithm, which is a spatial model for representing fine-grained parallel computations, is used for constructing self-replicating structures in a cellular space. The use of this model allows one to create more compact (in terms of the number of cell states and transition rules) and structured self-reproduction programs compared to the classical cellular automaton model. Two parallel substitution algorithms for modeling the self-reproduction of a cellular structure having the shape of a rectangular loop are presented. One of them models the self-reproduction of the original structures from left to right, and the other, from left to right and from bottom to top.

Journal ArticleDOI
TL;DR: The fundamental diagram obtained by simulation shows that the maximum flow more approaches to the observed data than that of the NaSch model, indicating that the presented model is more reasonable and realistic.
Abstract: A modified cellular automaton model for traffic flow was proposed. A novel concept about the changeable security gap was introduced and a parameter related to the variable security gap was determined. The fundamental diagram obtained by simulation shows that the maximum flow more approaches to the observed data than that of the NaSch model, indicating that the presented model is more reasonable and realistic.

Journal ArticleDOI
TL;DR: It is shown that globally synchronized period-three oscillations can be obtained if the lattice size L is a multiple of the spatial periodicity S(Λ) of the domain.
Abstract: Using a genetic algorithm a population of one-dimensional binary cellular automata is evolved to perform a computational task for which the best evolved rules cause the concentration to display a period-three oscillation. One run is studied in which the final state reached by the best evolved rule consists of a regular pattern or domain Λ, plus some propagating particles. It is shown that globally synchronized period-three oscillations can be obtained if the lattice size L is a multiple of the spatial periodicity S(Λ) of the domain. When L=m.S(Λ)-1 there is a cyclic particle reaction that keeps the system in two different phases and the concentration has a temporal periodicity that depends on the lattice size. The effects of random noise on the evolved cellular automata has also been investigated.

Patent
17 Feb 2004
TL;DR: In this article, a cellular automata-based model is proposed for spatial structure analysis of protein that helps efficient drug discovery by shortening a time span bottlenecking existing techniques while ensuring practical accuracy.
Abstract: PROBLEM TO BE SOLVED: To provide a computerized technique for a spatial structure analysis of protein that helps efficient drug discovery by shortening a time span bottlenecking existing techniques while ensuring practical accuracy. SOLUTION: A proposed model based on a cellular automaton method is a discrete three-dimensional model with layered hexagonal lattice planes, and unit cells have information on a contained amino acid and its accompanying charge and mass. The transition of the unit cells depends on a vector sum from the surrounding cells. The mobility of the unit cells also varies with temperature. The framework represents the structure of protein. COPYRIGHT: (C)2005,JPO&NCIPI

Journal ArticleDOI
Jan Lunze1
TL;DR: For stochastic automata it is impossible to perform this reduction in such a way that the observation result for the remaining states remains unchanged, and the state observation algorithm applied to the reduced automaton does not generate the same probability distribution as for the original automaton.


Journal Article
TL;DR: In this article, the authors present an implementation of the blob object using the programmable matter platform of cellular automaton simulation, and then they describe the implementation of Blob division, the machine implementation of compute node duplication, all explained in separate boxes.
Abstract: This work is part of the Blob computing project whose goal is to develop a new model of parallel machine including a new model of computation and a new machine. The whole project idea is to try to capture basic principles of bio-computing system allowing massive parallelism. The model of computation is based on the concept of self-developing network of compute nodes, the machine is a 2-D cellular automaton grid whose evolution rule is fixed and implemented by simplified physical laws. A machine configuration represents idealized physical objects such as membrane or particle gas. A central object called blob is the harware image of a compute node. Based on published formal proof, this paper presents first an implementation of the blob object using the programmable matter platform of Cellular Automaton simulation. Then it describes an implementation of Blob division, the machine implementation of compute node duplication. We used five different kinds of cellular automaton rules, all explained in separate boxes. The result obtained can be classified as a new specific form of self-reproducing cellular automaton. Unlike past examples of self-reproduction, it happens in parallel, since the number of time steps necessary is proportional to √(p), where p measures the information (number of bits) contained in the object to duplicate.

Journal ArticleDOI
TL;DR: The Game of Life is incredibly intriguing, giving rise to complex behavior that is visually stimulating, mathematically interesting and, moreover, it is known to be capable of universal computation.
Abstract: Cellular automata are collections of cells arranged in some manner such that each cell contains a value that is updated from generation to generation according to a local rule. The Game of Life [1-5,7,15] is perhaps the best known cellular automaton. It is based upon a rectangular arrangement of cells that are either 0 or 1, along with simple rules of evolution: if a cell is 0 and has exactly 3 immediate neighbors then it becomes a 1; if a cell is 0 and has exactly 2 or 3 immediate neighbors that are 1, then the cell remains 1; otherwise, the cell becomes or remains 0. The Game of Life is incredibly intriguing, giving rise to complex behavior that is visually stimulating, mathematically interesting and, moreover, it is known to be capable of universal computation. Despite the fact that at a basic level it was designed to model alive and dead cells, it is primarily a toy model in the sense that it does not model any physical behavior well.

Journal Article
TL;DR: It is shown that the reachability problem for a finite state automaton interacting with a quadrant of the plane extended by a power function, a polynomial function or a linear function is algorithmically undecidable, by simulating a Minsky machine.
Abstract: In this paper we study the model of a finite state automaton interacting with infinite two-dimensional geometric environments. We show that the reachability problem for a finite state automaton interacting with a quadrant of the plane extended by a power function, a polynomial function or a linear function is algorithmically undecidable, by simulating a Minsky machine. We also consider the environment defined by a parabola which impedes the direct simulation of multiplication. However we show that the model of a finite automaton interacting inside a parabola is also universal.

Journal ArticleDOI
TL;DR: A set of theorem about the evolutionary properties of the automaton networks are presented, which includes the theorems that, for an additive automaton network, the tree structures are identical, and that the geometric entropy equals to its topological entropy.
Abstract: A set of theorems about the evolutionary properties of the automaton networks are presented in this article, which includes the theorems that, for an additive automaton network, the tree structures are identical, and that the geometric entropy equals to its topological entropy. The exact analytical formula for the entropy of the additive automaton networks is introduced, and applied to investigate the evolutionary properties of the elementary cellular automata of number 90 and number 150.

Journal ArticleDOI
TL;DR: This work has shown the order of the states of a finite automaton is shown to be graduated, and the well-known Cerny problem on the minimal length of reset words can be formulated in terms of global height.
Abstract: The states of a finite automaton are ordered by height. This order is shown to be graduated, and the well-known Cerny problem on the minimal length of reset words can be formulated in terms of global height. The problem is proved for automata with four states.