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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TL;DR: In this paper , it was shown that one can learn automata with a number of states that is exponential in the amount of data available, which is in sharp contrast with the established understanding of the sample complexity of automata, described in terms of the overall number of state and input letters.
Abstract: Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as complex systems made of many components, each implementing a specific functionality. Any automaton can serve as a component; using specific components allows for a fine-grained control of the expressivity of the resulting class of automata; using prime automata as components implies specific expressivity guarantees. Moreover, specifying automata as cascades allows for describing the sample complexity of automata in terms of their components. We show that the sample complexity is linear in the number of components and the maximum complexity of a single component, modulo logarithmic factors. This opens to the possibility of learning automata representing large dynamical systems consisting of many parts interacting with each other. It is in sharp contrast with the established understanding of the sample complexity of automata, described in terms of the overall number of states and input letters, which implies that it is only possible to learn automata where the number of states is linear in the amount of data available. Instead our results show that one can learn automata with a number of states that is exponential in the amount of data available.
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07 Jul 2003TL;DR: The main properties of the quasi-product concerning homomorphic and metric representation of tree automata are presented, and the representing powers of special quasi-products are compared.
Abstract: Products of tree automata do not preserve the basic properties of homomorphically and metrically complete systems of finite state automata. To remedy it, we have introduced the concept of the quasi-product of tree automata which is only a slightly more general than the product. In this paper we present the main properties of the quasi-product concerning homomorphic and metric representation of tree automata, and compare the representing powers of special quasi-products.
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TL;DR: It is shown that the families of sets accepted by the product or the sum type are always incomparable.
Abstract: The authors previously introduced the following two-dimensional automaton, and made several discussions on its accepting power. The input two-dimensional tape is rotated by 90, 180 or 270 deg in clockwise direction. The rotated results are scanned by one-dimensional bounded cellular acceptors. The results of scanning are combined by product (∧) or sum (∨), to make the decision regarding the final acceptance. The purpose of this paper is to discuss further details of the accepting power of such an automaton. In the first-half of this paper, the situation is assumed where the rotated inputs are scanned by the deterministic one-dimensional bounded cellular acceptors. A discussion is made on the relation between the accepting powers when the results of the scanning are combined only by product or only by sum. It is shown that the families of sets accepted by the product or the sum type are always incomparable. In the second half of the paper, the relation between the accepting powers of the following two automata are described. One is the automaton obtained by combining the one-dimensional bounded cellular acceptors by sum (or product); the other is the automaton obtained by combining one-way parallel sequential array acceptors by sum (or product).
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TL;DR: This review deals with the theory and practice of discrete automata, especially with transition processes and hazardous races in such automata.
Abstract: This review deals with the theory and practice of discrete automata, especially with transition processes and hazardous races in such automata.