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Showing papers on "Continuous automaton published in 1990"


Journal ArticleDOI
TL;DR: In this paper, Park, Steiglitz and Thurston studied the evolution of an arbitrary initial configuration of a certain filter cellular automaton introduced by Park and Stehlitz and found that the interaction properties of these particles are richer than the usual solitons.

43 citations


Journal ArticleDOI
TL;DR: A deterministic version of the cellular automaton first shown to display self-organized criticality is studied, showing that there exist many coexisting periodic attractors, with a period that is independent of initial condition.
Abstract: We study a deterministic version of the cellular automaton first shown to display self-organized criticality. Detailed analysis shows that there exist many coexisting periodic attractors, with a period that is independent of initial condition. This leads us to picture the critical state as the union of many such coexisting, neutrally stable orbits. Dhar's recently developed formalism [Phys. Rev. Lett. 64, 1613 (1990)] can be used to explain many of the observed regularities.

30 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider a cellular automaton where each lattice site may take on one ofN values, referred to as colors, arranged in a cyclic hierarchy, meaning that colork follows colork−1 modN (k=0,..., n−1).
Abstract: Consider a cellular automaton defined on ℤ where each lattice site may take on one ofN values, referred to as colors. TheN colors are arranged in a cyclic hierarchy, meaning that colork follows colork−1 modN (k=0,...,N−1). Any two colors that are not adjacent in this hierarchy form an inert pair. In this scheme, there is symmetry in theN colors. Initialized the cellular automaton with product measure, and let time pass in discrete units. To get the configuration at timet+1 from the one at timet, each lattice site looks at the colors of its two nearest neighbors, and if it sees the color that follows its own color, then that site changes color to the color that follows; otherwise, that site does not change color. All such updates occur synchronously at timet+1. For each value ofN≥2, the fundamental question is whether each site in the cellular automaton changes color infinitely often (fluctuation) or only finitely often (fixation). We prove here that ifN≤4, then fluctuation occurs, and ifN≥5, then fixation occurs.

29 citations


Journal ArticleDOI
TL;DR: The traces of two-way computations which begin and finish at one or the other of the two ends of the input tape are characterized, and formulas are given which tell how traces are combined when the corresponding inputs are concatenated.
Abstract: Computations of a two-way automaton on an input tape are studied using the algebraic notion of trace ofa two-way computation {due to J. P. Pécuchet), and certain \"réductions\" of traces. This paper only deals with two-way computations which begin and finish at one or the other of the two ends of the input tape. The traces of such computations are characterized, and formulas are given which tell how traces are combined when the corresponding inputs are concatenated. Another tool for studying a two-way automaton (also due to Pécuchet) is the language of its control unit (considered over a \"double alphabet\"). This \"control language\" détermines the entire two-way automaton and this leads to formulas relating the control language and the language accepted by the two-way automaton itself. Résumé. Nous étudions les calculs d'un automate boustrophedon en employant la notion de trace d'un calcul {due à J. P. Pécuchet) et certaines « réductions » de traces. Cet article ne considère que les calculs boustrophedons qui commencent et finissent à l'un ou l'autre bout de la bande d'entrée. Nous décrivons les traces des calculs de ce type et donnons des formules qui indiquent comment se combinent les traces lorsque les entrées correspondantes sont concaténées. Un autre instrument dans l'étude des automates boustrophedons (dû aussi à J. P. Pécuchet) est le langage de l'unité de contrôle (exprimé sur un « double alphabet »). Ce « langage de contrôle » détermine l'automate boustrophedon et ceci conduit à des formules reliant le langage de contrôle et le langage accepté par l'automate boustrophedon. (*) Received June 1987, revised March 1988. This research was supported in part by U.S. Army Grant DAAG-29-85-K-0099 and U.S. Air Force Grant AFOSR-85-0186 through the Center for Mathematical System Theory, University of Florida, Gainesville, FL 32611. (*) Computer Science Department, University of Nebraska, Lincoln, NE 68588, U.S.A. Informatique théorique et Applications/Theoretical Informaties and Applications 0988-3754 90/01 47 20/S4.00/© AFCET Gauthier-Villars

18 citations



Proceedings ArticleDOI
17 Jun 1990
TL;DR: A theory of learning automata that is applicable to studying goal-seeking systems of many types and has been expanded to include infinite sets of states is developed.
Abstract: The authors have been developing a theory of learning automata that is applicable to studying goal-seeking systems of many types. The stepwise convergence of such systems to a goal state can be mapped into the training sequences of an appropriate learning automaton. This theory has been expanded to include infinite sets of states. The learning automaton may have an infinite characteristic semigroup of state transitions. The algebraic properties of the automaton are determined by this semigroup. A topology is introduced into the characteristic semigroup, S '. The latter can be considered as a function space of transformations of S . Behavior characteristics of the learning automaton be defined rigorously. In special cases, they can be related to the topological properties of S ' and S , such as continuity of the transition function, separation properties and compactness

1 citations


Journal ArticleDOI
TL;DR: An algorithm is proposed reducing the problem of analytical determination of ternARY processes on automaton outputs and inside the automaton from given ternary processes on the Automaton inputs to standard determination of the processes in an automaton with the alphabet.
Abstract: The paper examines a digital automaton with memory operating in the ternary alphabet (0, 1, θ). The problem of analytical determination of ternary processes on automaton outputs and inside the automaton from given ternary processes on the automaton inputs is considered. An algorithm is proposed reducing this problem to standard determination of the processes in an automaton with the alphabet (0, 1).