Showing papers on "Continuous automaton published in 1996"
TL;DR: In this paper, it was shown that there is no nontrivial, homogeneous, local, unitary, scalar cellular automata in one dimension, and that the homogeneity condition can be overcome by a quantum cellular automaton with exactly unitary partitioning.
Abstract: A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one-parameter family of evolution rules which are best interpreted as those for a one-particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second, of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.
730 citations
TL;DR: A direct connection between a cellular automaton and integrable nonlinear wave equations is shown and a general method for constructing suchintegrable cellular automata and their $N$-soliton solutions is proposed.
Abstract: We show a direct connection between a cellular automaton and integrable nonlinear wave equations. We also present the $N$-soliton formula for the cellular automaton. Finally, we propose a general method for constructing such integrable cellular automata and their $N$-soliton solutions.
505 citations
TL;DR: A simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg is examined, pointing out important parameters defining the shape of the fundamental diagram and investigating the importance of stochastic elements with respect to real life traffic.
Abstract: We examine a simple two-lane cellular automaton based upon the single-lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.
440 citations
TL;DR: It is proved that every reversible two-dimensional cellular automaton can be expressed as a combination of four block permutations, and some shift-like mappings.
Abstract: We demonstrate the structural invertibility of all reversible one- and two-dimensional cellular automata. More precisely, we prove that every reversible two-dimensional cellular automaton can be expressed as a combination of four block permutations, and some shift-like mappings. Block permutations are very simple functions that uniformly divide configurations into rectangular regions of equal size and apply a fixed permutation on all regions.
91 citations
TL;DR: This poster presents a probabilistic simulation of the response of the immune system to EMTs to treat central nervous system injuries and shows clear patterns of response to EMMARM.
Abstract: Reference EPFL-ARTICLE-28529doi:10.1103/PhysRevLett.77.4969View record in Web of Science Record created on 2004-11-30, modified on 2016-09-30
82 citations
TL;DR: In this paper, the structure of the soliton cellular automaton is studied by means of combinatorial techniques, and it is shown that the shape of the Young tableaux gives an infinite number of time invariants of the automaton.
66 citations
TL;DR: A probabilistic synthesis algorithm for determining such a linear hybrid cellular automaton with a specific characteristic polynomial is given, along with empirical results and a theoretical analysis.
Abstract: The paper studies theoretical aspects of one dimensional linear hybrid cellular automata over a finite (Galois) field. General results concerning the characteristic polynomials of such automata are presented. A probabilistic synthesis algorithm for determining such a linear hybrid cellular automaton with a specific characteristic polynomial is given, along with empirical results and a theoretical analysis. Cyclic boundary cellular automata are defined and related to the more common null boundary cellular automate. An explicit similarity transform between a cellular automaton and its corresponding linear feedback shift register is derived.
54 citations
TL;DR: This work designs a reversible PCA SR 8, a special type of CA whose cell is divided into five parts, and shows that various objects can reproduce themselves in a very simple manner.
48 citations
01 Aug 1996
TL;DR: A multimodal searching technique based on a stochastic automaton where the environment where the automaton operates corresponds to the function to be optimized which is assumed to be unknown function of a single parameter x.
Abstract: This paper describes a multimodal searching technique based on a stochastic automaton. The environment where the automaton operates corresponds to the function to be optimized which is assumed to be unknown function of a single parameter x. The admissible region of x is quantized into N subsets. The environment response is continuous (S-model). The complete set of actions of the automaton is divided into nonempty subsets. The action set is changing from instant to instant and is selected based on a probability distribution. These actions are in turn associated with the discrete values of the parameter x. Convergence and convergence rate results are presented. Simulation results illustrate the performance of this searching technique.
26 citations
22 Feb 1996
TL;DR: In this article, the authors introduce the linear quantum cellular automaton (LQCA) model and give an efficient algorithm to decide if a cellular automata is well-formed.
Abstract: In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is O(n2) if the input automaton has continuous neighborhood.
25 citations
TL;DR: In this paper, a general definition of damage spreading in a pair of models is presented, which is applied to the Domany-Kinzel cellular automaton in one dimension; the active phase of this model is shown to consist of three sub-phases, characterized by different damage-spreading properties.
Abstract: We present a general definition of damage spreading in a pair of models. Using this general framework, one can define damage spreading in an objective manner, that does not depend on the particular dynamic procedure that is being used. The formalism is applied to the Domany-Kinzel cellular automaton in one dimension; the active phase of this model is shown to consist of three sub-phases, characterized by different damage-spreading properties.
TL;DR: In this paper, the authors propose a bridge between the theory of exactly solvable models and the investigation of traffic flow by choosing the activities in an appropriate way, the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as spacetime trajectories of cars.
Abstract: We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow By choosing the activities in an appropriate way, the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as spacetime trajectories of cars This then allows for a calculation of the flow-density relationship (fundamental diagram) We further introduce a closely related cellular automaton model This model can be viewed as a variant of the Nagel - Schreckenberg model in which the cars do not have a velocity memory It is also exactly solvable and the fundamental diagram is calculated
07 Oct 1996
TL;DR: This paper discusses how logical universality can be obtained under the reversibility constraint, and shows the previous models of 16-state universal reversible CA, and explains how self-reproduction is possible in a reversible CA.
Abstract: A reversible cellular automaton (RCA) is a “backward deterministic” CA in which every configuration of the cellular space has at most one predecessor. Such reversible systems have a close connection to physical reversibility, and have been known to play an important role in the problem of inevitable power dissipation in computing systems. In this paper, we investigate problems of logical universality and self-reproducing ability in two-dimensional reversible cellular spaces. These problems will become much more important when one tries to construct nano-scaled functional objects based on microscopic physical law. Here, we first discuss how logical universality can be obtained under the reversibility constraint, and show our previous models of 16-state universal reversible CA. Next we explain how self-reproduction is possible in a reversible CA.
TL;DR: The design and the analysis of a new reinforcement scheme for learning automata and its application for multimodal functions optimization and simulation results show the feasibility and the good performance of this optimization technique.
Abstract: This paper deals with the design and the analysis of a new reinforcement scheme for learning automata and its application for multimodal functions optimization. This reinforcement scheme generalizes the well known Bush-Mosteller scheme with decreasing gain for learning automata with continuous inputs. The theoretical analysis is based on martingale theory. The conditions associated with the convergence of this scheme to the optimal pure strategy are stated, and the order of convergence rate is estimated. The variation domains of the variables of the function to be optimized are discretized into subsets which are associated to the outputs of the learning automaton. The values of the function on these subsets are used to construct the continuous automaton inputs. Simulation results show the feasibility and the good performance of this optimization technique.
Journal Article•
TL;DR: The results of investigation prove that any inflorescence of any kind can be constructed in two-dimensional asynchronous cellular automaton of any cell which has not more than 9 neighbours and notMore than 12 states; the number of the critical points when local transitions functions are transformed is bounded by three.
Abstract: The paper deals with the cellular automata models for the growth of diverse types of the inflorescences. Starting with the classic botanical classification of the inflorescences we design the models of inflorescences in two-dimensional cellular automata. The results of investigation prove that any inflorescence of any kind can be constructed in two-dimensional asynchronous cellular automaton of any cell which has not more than 9 neighbours and not more than 12 states; the number of the critical points when local transitions functions are transformed is bounded by three.
TL;DR: In this article, it was shown that for large values of the total time q = Σ u q u u u ǫ ∼ q as q → ∞ which corresponds to non-intermittent fluctuations.
Abstract: The large time behavior of stochastic cellular automata is investigated by means of an analogy with Van Kampen's approach to the ergodic behavior of Markov processes in continuous time and with a discrete state space. A stochastic cellular automaton with a finite number of cells may display an extremely large, but however finite number M of lattice configurations. Since the different configurations are evaluated according to a stochastic local rule connecting the variables corresponding to two successive time steps, the dynamics of the process can be described in terms of an inhomogeneous Markovian random walk among the M configurations of the system. An infinite Lippman-Schwinger expansion for the generating function of the total times q 1 , …, q M spent by the automaton in the different M configurations is used for the statistical characterization of the system. Exact equations for the moments of all times q 1 , …, q M are derived in terms of the propagator of the random walk. It is shown that for large values of the total time q = Σ u q u the average individual times 〈 q u 〉 attached to the different configurations u = 1, …, M are proportional to the corresponding stationary state probabilities P u st : 〈 q u 〉 ∼ q P u st , u = 1, …, M . These asymptotic laws show that in the long run the cellular automaton is ergodic, that is, for large times the ensemble average of a property depending on the configurations of the lattice is equal to the corresponding temporal average evaluated over a very large time interval. For large total times q the correlation functions of the individual sojourn times q 1 , …, q M increase linearly with the total number of time steps q : 〈 Δq u Δq u ′ 〉 ∼ q as q → ∞ which corresponds to non-intermittent fluctuations. An alternative approach for investigating the ergodic behavior of Markov processes in discrete space and time is suggested on the basis of a multiple averaging of a Kronecker symbol; this alternative approach can be extended to non-Markovian random processes with infinite memory. The implications of the results for the numerical analysis of the large time behavior of stochastic cellular automata are also investigated.
01 Jan 1996
TL;DR: In this article, the authors proposed a method for generating a discrete event model for a continuous-variable plant from experimental data by measuring sequences of qualitative values of the state variables yield a linear interval matrix equation which can be used to find bounds for the parameters of a linear state space model.
Abstract: The paper proposes a method for generating a discrete event model for a continuous-variable plant from experimental data Measured sequences of qualitative values of the state variables yield a linear interval matrix equation which can be used to find bounds for the parameters of a linear state space model The qualitative model in a form of nondeterministic automaton is then constructed from the identified interval system It can be ensured that the automaton generates all possible qualitative trajectories of the given system The method is illustrated by an application
TL;DR: Convergence and convergence rate results are presented using quasimartingales theory and the behaviour of a stochastic automaton operating in an S-model environment is described.
Abstract: The behaviour of a stochastic automaton operating in an S-model environment is described. The environment response takes an arbitrary value in the closed segment [0, 1] (continuous response). The learning automaton uses a reinforcement scheme to update its action probabilities on the basis of the reaction of the environment. The complete set of actions is divided into a collection of non-empty subsets. The action set is changing from instant to instant. Each action set is selected according to a given probability distribution. Convergence and convergence rate results are presented. These results have been derived using quasimartingales theory.
TL;DR: A new automaton rule is presented which calculates simultaneously all shortest paths between a starting position and a target cell, based on wave propagation, which ensures that the dynamics settles down in an equilibrium state which represents an optimal solution.
Abstract: Cellular automata are deterministic dynamical systems in which time, space, and state values are discrete. Although they consist of uniform elements, which interact only locally, cellular automata are capable of showing complex behavior. This property is exploited for solving path planning problems in workspaces with obstacles. A new automaton rule is presented which calculates simultaneously all shortest paths between a starting position and a target cell. Based on wave propagation, the algorithm ensures that the dynamics settles down in an equilibrium state which represents an optimal solution. Rule extensions include calculations with multiple starts and targets. The method allows applications on lattices and regular, weighted graphs of any finite dimension. In comparison with algorithms from graph theory or neural network theory, the cellular automaton approach has several advantages: Convergence towards optimal configurations is guaranteed, and the computing costs depend only linearly on the lattice ...
06 Aug 1996
TL;DR: A universal spatial automaton, called WAVE, for highly parallel processing in arbitrary distributed systems is described, based on a virus principle, which can easily model any other paradigms for parallel and distributed computing.
Abstract: A universal spatial automaton, called WAVE, for highly parallel processing in arbitrary distributed systems is described. The automaton is based on a virus principle where recursive programs, or waves, self-navigate in networks of data or processes in multiple cooperative parts while controlling and modifying the environment they exist in and move through. The layered general organisation of the automaton as well as its distributed implementation in computer networks are discussed. As the automaton dynamically creates, modifies, activates and processes any knowledge networks arbitrarily distributed in computer networks, it can easily model any other paradigms for parallel and distributed computing. Comparison of WAVE with some known programming models and languages, and ideas of their possible integration are also given.
TL;DR: Simulation results indicate the effectiveness of multilevel hierarchical systems of learning stochastic automata, and a learning scheme based on the Bush-Mosteller reinforcement scheme is used.
Abstract: Multilevel hierarchical systems of learning stochastic automata are investigated in this paper. The system under consideration consists of several levels of automata with different number of outputs. Each automaton is a variable-structure stochastic automaton. A learning scheme which is based on the Bush-Mosteller reinforcement scheme is used to adjust the probabilities associated with the actions of the automata of the hierarchical learning system. Boolean and continuous automaton inputs have been considered. Convergence and convergence rate analysis are presented. The optimization of multimodal functions using this multilevel system of automata is also described. Simulation results indicate the effectiveness of such multilevel learning systems.
11 Dec 1996
TL;DR: Conditions under which the automaton generated by a modification of the approximation algorithm from Niinomi et al. (1996) generates the exact language for the hybrid system are developed.
Abstract: It is known that one can not always have a finite state representation for hybrid systems and many decision properties can be undecidable It was shown in Cury et al (1995), however, that if one has a finite state automaton that generates an outer approximation to the hybrid system language, it may be possible to synthesize a discrete-state supervisor to control the hybrid system based on the approximating automaton using standard synthesis methods from the theory of discrete event systems (DESs) In this paper we develop conditions under which the automaton generated by a modification of the approximation algorithm from Niinomi et al (1996) generates the exact language for the hybrid system
TL;DR: The fractal dimension for the basin boundary set of the attracting configurations of cellular automata is found and obtained data allow us to qualify configurations from the attracting set.
Abstract: 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.
Journal Article•
TL;DR: A type of reversible cellular automaton is proposed, which can be used to discuss the question of irreversibility in statistical mechanics.
Abstract: A type of reversible cellular automaton is proposed, which can be used to discuss the question of irreversibility in statistical mechanics. It lives on an infinite lattice in space-time, whose nodes are points with integer coordinates, either all even or all odd, and whose edges join all pairs of nearest-neighbour nodes. The states of the edges in the immediate future of each node are related to those in its immediate past by a ‘dynamical rule’ which is deterministic and invertible. The assumed probability measure makes the nodes at time 0 independent, and correlations develop as the time variable t increases because of the dynamical rule. Two types of entropy are defined: one, analogous to the Gibbs entropy in statistical mechanics, is shown to be independent of t, while the other, analogous to Boltzmann entropy in statistical mechanics, can change with t and is shown to increase in the sense that it is minimal at t = 0.
05 Aug 1996
TL;DR: In this paper, a finite automaton and its applications are discussed, and then a fuzzy automaton model is proposed and the definition, theorems, fuzzy mapping ruler, homomorphism, and minimum states for implementation are given.
Abstract: In this paper, a finite automaton and its applications are first discussed, and then a fuzzy automaton model is proposed. In the fuzzy automaton model, the definition, theorems, fuzzy mapping ruler, homomorphism, and minimum states for implementation are given. In the last, some applications of a fuzzy automaton are illustrated with examples.
Journal Article•
TL;DR: There is no sequence of functions φN : CN → BN such thatπN and φ−1 N uniformly converge to continuous functions in such a topology.
Abstract: Let ω = {0, 1, . . . , n − 1} be a finite alphabet, DN = {1, 2, . . . ,N}, and BN = {x ∈ [0, 1] | ∃k ∈ ! : x = k/nN}. A configuration is a function of the form: ξ : DN → ω, and CN is the set of all configurations. Two configurations ξ1 and ξ2 are near if d(ξ1, ξ2) = (N −A)/N is small, where A = sup{p | ∃i ∈ {0, 1, . . . ,N} : ∀k = i + 1, i + 2, . . . , i + p ≤ N ξ1(k) = ξ2(k)}. The following results are proved. 1. There is no sequence of functions φN : CN → BN such that φN and φ−1 N uniformly converge to continuous functions in such a topology. 2. Evolutions of cellular automata (CA) cannot be approximated by the superpositions of real continuous functions. In the proofs of these results advantage was taken of some CA acting in " and in DN with a stationary boundary condition.