Topic
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: It is numerically found that the mean velocity of traffic continuously decreases with increasing concentration of cars, so that the global picture emerges in terms of asymptotic order, local jam and fluctuations.
Abstract: We present a cellular automaton model of traffic in a city where cars sit between crossings so that they never block the transversal movements. They turn with probability γ, 0⩽γ⩽1. The model is presented in two variants depending on the direction of the flow on the different streets. We numerically find that the mean velocity of traffic continuously decreases with increasing concentration of cars. For a given concentration the mean velocity is minimum for γ=0.5 in both variants of the model. Exact expressions for γ=0,0.5,1 are found for an infinite city and a global picture emerges in terms of asymptotic order, local jam and fluctuations.
15 citations
14 Aug 2012
TL;DR: It is remarked that the automaton F×3 that multiplies by 3 can be slightly modified to simulate the Collatz function and several open problems concerning pattern generation by cellular automata are state.
Abstract: We discuss one-dimensional reversible cellular automata F×3 and F×3/2 that multiply numbers by 3 and 3/2, respectively, in base 6. They have the property that the orbits of all non-uniform 0-finite configurations contain as factors all finite words over the state alphabet {0,1,…,5}. Multiplication by 3/2 is conjectured to even have an orbit of 0-finite configurations that is dense in the usual product topology. An open problem by K. Mahler about Z-numbers has a natural interpretation in terms the automaton F×3/2. We also remark that the automaton F×3 that multiplies by 3 can be slightly modified to simulate the Collatz function. We state several open problems concerning pattern generation by cellular automata.
15 citations
25 Mar 2002
TL;DR: Enough conditions are studied to ensure that an automaton operating in discrete-time refines a hybrid automaton with its underlying continuous time model, which provides the notion of refinement.
Abstract: Notations like hybrid automata are highly useful in the development process of hybrid systems to document requirements in early design steps. When it comes to implementation a part of the requirements will be realized in software in a discrete-time manner. We therefore study sufficient conditions which ensure that an automaton operating in discrete-time refines a hybrid automaton with its underlying continuous time model. Our notion of refinement provides that vital properties which have been established for the hybrid automaton also hold for its refinement. Furthermore, we outline a method how to derive a discrete-time refinement from a hybrid automaton.
15 citations
TL;DR: In this paper, a biochemical reaction system can be approximated by a multi-affine system or an affine system on a rectangle, and model checking can be employed to determine whether the dynamic behavior of the automaton satisfies specific properties.
15 citations
TL;DR: In this paper, the authors give conditions that force a probability measure, which is invariant for the -action of F and the shift map σ, to be the Haar measure on Σ, a closed shift-invariant subgroup of the abelian compact group.
Abstract: Let be a bipermutative algebraic cellular automaton. We present conditions that force a probability measure, which is invariant for the -action of F and the shift map σ , to be the Haar measure on Σ, a closed shift-invariant subgroup of the abelian compact group . This generalizes simultaneously results of Host et al (B. Host, A. Maass and S. Martinez. Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. Discrete Contin. Dyn. Syst. 9 (6) (2003), 1423–1446) and Pivato (M. Pivato. Invariant measures for bipermutative cellular automata. Discrete Contin. Dyn. Syst. 12 (4) (2005), 723–736). This result is applied to give conditions which also force an ( F , σ )-invariant probability measure to be the uniform Bernoulli measure when F is a particular invertible affine expansive cellular automaton on .
15 citations