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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.


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Dissertation
01 Oct 2012
TL;DR: It is shown that it is decidable whether a regular language of infinite trees is recognizable using a nondeterministic co-Buchi automaton, and a decision procedure is given to determine whether or not functions definable using weak or quasi-weak cost automata are equivalent up to the boundedness relation, which proves the decidability of the weak cost monadic logic over infinite trees.
Abstract: Cost automata are traditional finite state automata enriched with a finite set of counters that can be manipulated on each transition. Based on the evolution of counter values, a cost automaton defines a function from the set of structures under consideration to the natural numbers extended with infinity, modulo a boundedness relation that ignores exact values but preserves boundedness properties. Historically, variants of cost automata have been used to solve problems in language theory such as the star height problem. They also have a rich theory in their own right as part of the theory of regular cost functions, which was introduced by Colcombet as an extension to the theory of regular languages. It subsumes the classical theory since a language can be associated with the function that maps every structure in the language to 0 and everything else to infinity; it is a strict extension since cost functions can count some behaviour within the input. Regular cost functions have been previously studied over finite words and trees. This thesis extends the theory to infinite trees, where classical parity automata are enriched with a finite set of counters. Weak cost automata, which have priorities {0,1} or {1,2} and an additional restriction on the structure of the transition function, are shown to be equivalent to a weak cost monadic logic. A new notion of quasi-weak cost automata is also studied and shown to arise naturally in this cost setting. Moreover, a decision procedure is given to determine whether or not functions definable using weak or quasi-weak cost automata are equivalent up to the boundedness relation, which also proves the decidability of the weak cost monadic logic over infinite trees. The semantics of these cost automata over infinite trees are defined in terms of cost-parity games which are two-player infinite games where one player seeks to minimize the counter values and satisfy the parity condition, and the other player seeks to maximize the counter values or sabotage the parity condition. The main contributions and key technical results involve proving that certain cost-parity games admit positional or finite-memory strategies. These results also help settle the decidability of some special cases of long-standing open problems in the classical theory. In particular, it is shown that it is decidable whether a regular language of infinite trees is recognizable using a nondeterministic co-Buchi automaton. Likewise, given a Buchi or co-Buchi automaton as input, it is decidable whether or not there is a weak automaton recognizing the same language.

9 citations

Proceedings ArticleDOI
10 Jan 1995
TL;DR: A number of lemmas are provided that show that this relatively small number of operations is sufficient in many other cases in which the automata are not independent and it is shown how the automaton should be ordered to achieve this.
Abstract: This paper examines some numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the automata are completely independent, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by /spl rho//sub N/=/spl Pi//sub i=1//sup N/n/sub i//spl times//spl Sigma//sub i=1//sup N/n/sub i/, where n/sub i/ is the number of states in the i/sup th/ automaton and N is the number of automata in the network. We provide a number of lemmas that show that this relatively small number of operations is sufficient in many other cases in which the automata are not independent and we show how the automata should be ordered to achieve this. >

9 citations

Posted Content
TL;DR: In this paper, a variant of Hofstadter's Q-sequence is analyzed and shown to be 2-automatic, and an automaton for computing the sequence is explicitly given.
Abstract: Following up on a paper of Balamohan, Kuznetsov, and Tanny, we analyze a variant of Hofstadter's Q-sequence and show it is 2-automatic. An automaton computing the sequence is explicitly given.

9 citations

Book ChapterDOI
13 Jul 2011
TL;DR: This work considers two classes of automata: cyclic automata and Eulerian automata, and studies the computational complexity of the following problems: does there exist a reset word of given length for a given automaton?
Abstract: A word is called a reset word for a deterministic finite automaton if it maps all states of this automaton to one state. We consider two classes of automata: cyclic automata and Eulerian automata. For these classes we study the computational complexity of the following problems: does there exist a reset word of given length for a given automaton? what is the minimal length of the reset words for a given automaton?

9 citations

Journal ArticleDOI
TL;DR: The class of degree-languages over push-down automata (linear bounded automata) contains the intersection-closure and the complements of the context-free (context-sensitive) languages and it is contained in the Boolean closure of the contexts-free and context-sensitive languages.

9 citations


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