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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.


Papers
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Journal ArticleDOI
James W. Thatcher1, Jesse B. Wright1
TL;DR: The standard closure theorems are proved for the class of sets “recognizable” by finite algebras, and a generalization of Kleene's regularity theory is presented.
Abstract: Many of the important concepts and results of conventional finite automata theory are developed for a generalization in which finite algebras take the place of finite automata The standard closure theorems are proved for the class of sets “recognizable” by finite algebras, and a generalization of Kleene's regularity theory is presented The theorems of the generalized theory are then applied to obtain a positive solution to a decision problem of second-order logic

790 citations

Book ChapterDOI
18 Jul 2001
TL;DR: An algorithm to generate Buchi automata from LTL formulae is presented and compared with Spin: the experiments show that the algorithm is much more efficient than Spin.
Abstract: We present an algorithm to generate Buchi automata from LTL formulae. This algorithm generates a very weak alternating co-Buchi automaton and then transforms it into a Buchi automaton, using a generalized Buchi automaton as an intermediate step. Each automaton is simplified on-the-fly in order to save memory and time. As usual we simplify the LTL formula before any treatment. We implemented this algorithm and compared it with Spin: the experiments show that our algorithm is much more efficient than Spin. The criteria of comparison are the size of the resulting automaton, the time of the computation and the memory used. Our implementation is available on the web at the following address: http://verif.liafa.jussieu.fr/ltl2ba

725 citations

Proceedings ArticleDOI
29 May 1995
TL;DR: It is proved that the reachability problem is undecidable for timed automata augmented with a single stopwatch, and an (optimal) PSPACE reachability algorithm is given for the case of initialized rectangular automata.
Abstract: Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify the precise boundary between decidability and undecidability of the reachability problem for hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes. Our algorithm is based on the construction of a timed automaton that contains all reachability information about a given initialized rectangular automaton. The translation has practical significance for verification, because it guarantees the termination of symbolic procedures for the reachability analysis of initialized rectangular automata. The translation also preserves the $\omega$-languages of initialized rectangular automata with bounded nondeterminism. On the negative side, we show that several slight generalizations of initialized rectangular automata lead to an undecidable reachability problem. In particular, we prove that the reachability problem is undecidable for timed automata augmented with a single stopwatch.

685 citations

01 Jan 1966
TL;DR: The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem and a theory of communication is proposed that yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata.
Abstract: The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem. The argument proceeds as follows: 1. We assume the following postulates: a) there exists an upper bound on the speed of signals; b) there exists an upper bound on the density with which information can be stored. 2. Automata of fixed, finite size can recognize, at best, only iteratively defined classes of input sequences. (See Kleene (11) and Copi, Elgot, and Wright (8).) 3. Recursively defined classes of input sequences that cannot be defined iteratively can be recognized only by automata of unbounded size. 4. In order for an automaton to solve a (soluble) recursive problem, the possibility must be granted that it can be extended unboundedly in whatever way might be required. 5. Automata (as actual hardware) formulated in accordance with automata theory will, after a finite number of extensions, conflict with at least one of the postulates named above. Suitable conceptual structures for an exact theory of communication are then discussed, and a theory of communication proposed. All of the really useful results of automata theory may be expressed by means of these new concepts. Moreover, the results retain their usefulness and the new nrocedure has definite advantages over the older ones. The proposed representation differs from each of the presently known theories concerning information on at least one of the following essential points: 1. The existence of a metric is assumed for either space nor time nor for other physical magnitudes. 2. Time is introduced as a strictly local relation between states. 3. The objects of the theory are discrete, and they are combined and produced only by means of strictly finite techniques. The following conclusions drawn from the results of this work may be cited as of some practical interest: 1. The tolerance requirements for the response characteristics of computer components can be substantially weakened if the computer is suitably structured. 2. It is possible to design computers structurally in such a way that they are asynchronous, all parts operating in parallel, and can be extended arbitrarily without interrupting their computation. 3. For complicated organizational processes of any given sort the theory yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata. Diese Arbeit befasst sich mit den begrifflichen Grundlagen einer Theorie der Kommunikation. Die Aufgabe dieser Theorie soll es sein, moglichst viele Erscheinungen bei der Informationsubertragung und Informationswandlung in einheitlicher und exakter Weise zu beschreiben.

581 citations

Journal ArticleDOI
TL;DR: Algorithms are presented for converting a state graph describing thebehavior of an automaton to a regular expression describing the behavior of the same automaton, and for converting an regular expression into a stategraph.
Abstract: Algorithms are presented for 1) converting a state graph describing the behavior of an automaton to a regular expression describing the behavior of the same automaton (section 2), and 2) for converting a regular expression into a state graph (sections 3 and 4). These algorithms are justified by theorems, and examples are given. The first section contains a brief introduction to state graphs and the regular-expression language.

567 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
202219
20201
20191
20185
201748