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: Alur et al. as discussed by the authors proposed timed automata to model the behavior of real-time systems over time, and showed that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the non-deterministic case and PSPACE-complete in deterministic case.

7,096 citations

01 Jan 1962

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: 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.
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.

2,523 citations

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TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.

Abstract: Finite automata are considered in this paper as instruments for classifying finite tapes. Each one-tape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms.

1,930 citations

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01 Jan 2012

TL;DR: The introduction to formal languages and automata wasolutionary rather than rcvolrrtionary and addressed Initially, I felt that giving solutions to exercises was undesirable hecause it lirrritcd the Chapter 1 fntroduction to the Theory of Computation.

Abstract: G' A. Linz, Peter. An introduction to formal languages and automata / Peter Linz'--3'd cd charrgcs ftrr the second edition wercl t)volutionary rather than rcvolrrtionary and addressed Initially, I felt that giving solutions to exercises was undesirable hecause it lirrritcd the Chapter 1 fntroduction to the Theory of Computation. Issuu solution manual to introduction to languages. Introduction theory computation 2nd edition solution manual sipser. Structural Theory of automata: solution manual of theory of computation. Kellison theory of interest pdf. Transformation, Sylvester's theorem(without proof), Solution of Second Order. Linear Differential Higher Engineering Mathematics by B.S. Grewal, 40th Edition, Khanna. Publication. 2. Introduction Of Automata Theory, Languages and computationHopcroft. Motwani&Ulman UNIX system Utilities manual. 4.

1,383 citations

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TL;DR: The formalism of regular expressions was introduced by S. C. Kleene to obtain the following basic theorems.

Abstract: The formalism of regular expressions was introduced by S. C. Kleene [6] to obtain the following basic theorems.

1,132 citations