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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: This paper introduces two transition systems as semantics of the automaton, and derives necessary and sufficient conditions for a predicate to be control-invariant and shows that there always exists the supremal control-Invariant subpredicate for any predicate.
Abstract: Silva and Krogh formulate a sampled-data hybrid automaton to deal with time-driven events and discuss its verification. In this paper, we consider a state feedback control problem of the automaton. First, we introduce two transition systems as semantics of the automaton. Next, using these transition systems, we derive necessary and sufficient conditions for a predicate to be control-invariant. Finally, we show that there always exists the supremal control-invariant subpredicate for any predicate.
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TL;DR: An automaton is isomorphic to the direct product of a permutation stronglyconnected automaton and a synchronizing strongly connected automaton if and only if all of the following conditions are met.
Abstract: An automaton is isomorphic to the direct product of a permutation strongly connected automaton and a synchronizing strongly connected automaton if and only if all of the following conditions are met: (i) it is strongly connected; (ii) the minimal ideal of its transition semigroup is a right group and (iii) the ranges of the idempotent elements of the minimal ideal of its transition semigroup form a partition on its set of states.
TL;DR: There appears the second-order transition between B-saturated and steady reactive phase, which fails to be predicted by pure site-approximation mean-field approach, and the conclusion is made that such a kinetic behavior may be explained by fluctuations in number space.
Abstract: Computer simulations are introduced in the frame of site-approximation mean-field rate equations and applied to an A–B2 surface-reaction-like cellular automaton model. There appears the second-order (continuous) transition between B-saturated and steady reactive phase, which fails to be predicted by pure site-approximation mean-field approach. The conclusion is made that such a kinetic behavior may be explained by fluctuations in number space.
TL;DR: The problem of determination of the conditions of formation and splitting of a collective (a team) and the problem ofdetermination of the response of a dynamic automaton to specified input processes are shown to be equivalent.
Abstract: The problem of determination of the conditions of formation and splitting of a collective (a team) and the problem of determination of the response of a dynamic automaton to specified input processes are shown to be equivalent. Based on this fact, an automaton model of a collective is constructed. The apparatus of continuous logic and logical determinants are used to analyze the model.