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Continuous automaton
About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.
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TL;DR: A number-conserving partitioned cellular automaton (NC-PCA) is defined, which is divided into three parts, and each cell is represented by a triple of non-negative integers, and it is shown that Minsky's 3n time solution can be embedded into an NC- PCA, having an integer at most 9 in each part of a cell.
Abstract: We study the Firing Squad Synchronization Problem (FSSP) on a cellular automaton (CA) having number-conservation property In a number-conserving CA, all states of cells are represented by (tuples of) non-negative integers and the total number of its configuration is conserved throughout its computing processes But, if we use a usual framework of CA in which each state of a cell is represented by a single integer, it is not possible to make every cell to be in the same firing state, which should be different from the soldier state, under the usual FSSP condition without violating the number-conservativeness So, we employ the framework of a partitioned cellular automaton, and define a number-conserving partitioned cellular automaton (NC-PCA) Its cell is divided into three parts, and hence each cell is represented by a triple of non-negative integers In NC-PCA, only the constraint that the local transition function should satisfy a number-conserving condition is supposed Thus, it makes relatively easy to construct an NC-PCA Because each cell can hold three non-negative integers, it is possible to represent different states even if the sum of three numbers are equal Using this technique, we show that Minsky's 3n time solution can be embedded into an NC-PCA, having an integer at most 9 in each part of a cell
11 citations
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TL;DR: In this paper, the dynamics of a two-dimensional cellular automaton for the Moore neighborhood (eight closest neighbors of each cell) under fully asynchronous dynamics (where one single random cell updates at each time step).
Abstract: Cellular automata are usually associated with synchronous deterministic dynamics, and their asynchronous or stochastic versions have been far less studied although significant for modeling purposes. This paper analyzes the dynamics of a two-dimensional cellular automaton, 2D Minority, for the Moore neighborhood (eight closest neighbors of each cell) under fully asynchronous dynamics (where one single random cell updates at each time step). 2D Minority may appear as a simple rule, but It is known from the experience of Ising models and Hopfield nets that 2D models with negative feedback are hard to study. This automaton actually presents a rich variety of behaviors, even more complex that what has been observed and analyzed in a previous work on 2D Minority for the von Neumann neighborhood (four neighbors to each cell) (2007) This paper confirms the relevance of the later approach (definition of energy functions and identification of competing regions) Switching to the Moot e neighborhood however strongly complicates the description of intermediate configurations. New phenomena appear (particles, wider range of stable configurations) Nevertheless our methods allow to analyze different stages of the dynamics It suggests that predicting the behavior of this automaton although difficult is possible, opening the way to the analysis of the whole class of totalistic automata
11 citations
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11 citations
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TL;DR: A simplified cellular model for computer network, namely the NaSch network model, is proposed, which is originated at the Na Sch model of road traffic and consists of two kinds of cells, i.e. node cell and link cell.
11 citations
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TL;DR: The first rigorous proofs of two of Kauffman's generalizations about a random Boolean cellular automaton are given: a large fraction of vertices stabilize quickly, consequently the length of cycles in the automaton's behavior is small compared to that of a random mapping with the same number of states.
Abstract: Based on computer simulations, Kauffman (Physica D, 10, 145-156, 1984) made several generalizations about a random Boolean cellular automaton which he invented as a model of cellular metabolism. Here we give the first rigorous proofs of two of Kauffman's generalizations: a large fraction of vertices stabilize quickly, consequently the length of cycles in the automaton's behavior is small compared to that of a random mapping with the same number of states; and reversal of the states of a large fraction of the vertices does not affect the cycle to which the automaton moves. © 1991 Wiley Periodicals, Inc.
11 citations