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Showing papers on "Continuous automaton published in 2019"


Journal ArticleDOI
TL;DR: This paper investigates a specific reversible ETPCA, T0347, where 0347 is its identification number in the class of 256 ETPCAs, and shows that a glider, which is a space-moving pattern, and glider guns exist in this cellular space.
Abstract: We study a simple triangular partitioned cellular automaton (TPCA), and clarify its complex behavior. It is a CA with triangular cells, each of which is divided into three parts. The next state of a cell is determined by the three adjacent parts of its neighbor cells. This framework makes it easy to design reversible triangular CAs. Among them, isotropic and eight-state (i.e., each part has only two states) TPCAs are called elementary TPCAs (ETPCAs). They are extremely simple, since each of their local transition functions is described by only four local rules. In this paper, we investigate a specific reversible ETPCA $$T_{0347}$$ , where 0347 is its identification number in the class of 256 ETPCAs. In spite of the simplicity of the local function and the constraint of reversibility, evolutions of configurations in $$T_{0347}$$ have very rich varieties. It is shown that a glider, which is a space-moving pattern, and glider guns exist in this cellular space We also show that the trajectory and the timing of a glider can be fully controlled by appropriately placing stable patterns called blocks. Furthermore, using gliders to represent signals, we can implement universal reversible logic gates in it. By this, computational universality of $$T_{0347}$$ is derived.

9 citations


Posted Content
TL;DR: A generalization of this result can be applied to show that finitely generated subgroups and subsemigroups as well as principal left ideals of automaton semigroups are infinite if and only if there is an $\omega$-word with an infinite orbit under their action.
Abstract: We study the orbits of right infinite or $\omega$-words under the action of semigroups and groups generated by automata. We see that an automaton group or semigroup is infinite if and only if it admits an $\omega$-word with an infinite orbit, which solves an open problem communicated to us by Ievgen V. Bondarenko. In fact, we prove a generalization of this result, which can be applied to show that finitely generated subgroups and subsemigroups as well as principal left ideals of automaton semigroups are infinite if and only if there is an $\omega$-word with an infinite orbit under their action. We also discuss the situation in self-similar semigroups and groups and present some applications of the result. Additionally, we investigate the orbits of periodic and ultimately periodic words as well as the existence of $\omega$-words whose orbit is finite.

1 citations