Topic
ω-automaton
About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.
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25 Aug 1997
TL;DR: The meaning of sensitivity and its implications in CA behavior are discussed and an experimental evidence of the fact that sensitivity is linked to the fractal dimension of the space-time pattern generated by cellular automata evolutions is provided.
Abstract: In this paper we discuss the meaning of sensitivity and its implications in CA behavior. A new shift-invariant metric is given. The metric topology induced by this metric is perfect but not compact. Moreover we prove that the new space is “suitable” for the study of the dynamical behavior of CA. In this context sensitivity assumes a stronger meaning than before (usually S ZZ is given the product topology). Now cellular automata are sensitive if they are not only capable of “transporting” the information but if they are also able to create new information. We also provide an experimental evidence of the fact that (in the new topology) sensitivity is linked to the fractal dimension of the space-time pattern generated by cellular automata evolutions.
31 citations
TL;DR: This paper focuses on quantum analogues of various models of counter automata, and almost completely proves the relation between the classes of languages recognizable by bounded error quantum ones and classical deterministic ones in every model ofcounter automata.
31 citations
TL;DR: A direct proof is given that shows that (one-way) 3-head deterministic finite automata are computationally more powerful than 2-head finite automaton.
Abstract: A direct proof is given that shows that (one-way) 3-head deterministic finite automata are computationally more powerful than 2-head finite automata.
31 citations
TL;DR: The collective behavior of finite state stochastic automata is considered, which is of interest in view of the possibility of modeling group behavior of subjects in terms of these automata.
Abstract: The collective behavior of finite state stochastic automata is considered, which is of interest in view of the possibility of modeling group behavior of subjects in terms of these automata. The natural language for considering the collective behavior is that of game theory. After a brief introduction to a class of deterministic automata, the stochastic automaton is formulated and a nonlinear reinforcement specified. The finite state stochastic automaton is first considered in a game with nature, and conditions under which the automaton's winnings reach the Von Neumann value of the game are established. Next, two stochastic automata with an arbitrary number of states for each are considered in a game, the game matrix being specified. Performance of the automata for various conditions on the elements of the game matrix is considered. In a comparison of performance with deterministic automata, it is established that, for performance comparable to that of the finite state stochastic automaton, the deterministic automaton needs an infinite number of states. Finally, some games are simulated on a computer which verifies the general analysis and further sheds light on the details of the game.
31 citations
TL;DR: In this paper, the authors introduce two series of finite automata starting from the so-called Aleshin and Bellaterra automata, and prove that transformations defined by automata from the first series generate a free non-Abelian group of infinite rank.
Abstract: We introduce two series of finite automata starting from the so-called Aleshin and Bellaterra automata. We prove that transformations defined by automata from the first series generate a free non-Abelian group of infinite rank, while automata from the second series give rise to the free product of infinitely many groups of order 2.
30 citations