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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
01 Dec 2008
TL;DR: The notion of “don’t cares” for bdds to word languages as a means to reduce the automata sizes is generalized to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdbas.
Abstract: Automata have proved to be a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, analogous to the use of binary decision diagrams (bdds) to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this article, we generalize the notion of "don't cares" for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Buchi automaton (wdba) with respect to a given don't care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don't cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdbas.

10 citations

Book ChapterDOI
26 Aug 2002
TL;DR: Evidence is gathered that the cardinalitytheorem might also hold for finite automata, which states that a language is recursive if a Turing machine can exclude for any n words one of the n + 1 possibilities for the number of words in the language.
Abstract: Kummer's cardinalitytheorem states that a language is recursive if a Turing machine can exclude for any n words one of the n + 1 possibilities for the number of words in the language. This paper gathers evidence that the cardinalitytheorem might also hold for finite automata. Three reasons are given. First, Beigel's nonspeedup theorem also holds for finite automata. Second, the cardinalitytheorem for finite automata holds for n = 2. Third, the restricted cardinalitytheorem for finite automata holds for all n.

10 citations

Journal ArticleDOI
TL;DR: It is proved that the class of deterministic Data Walking Automata is closed under all Boolean operations, and that theclass of non-deterministic Data walking Automata has decidable emptiness, universality, and containment problems.
Abstract: Data words are words with additional edges that connect pairs of positions carrying the same data value. We consider a natural model of automaton walking on data words, called Data Walking Automaton, and study its closure properties, expressiveness, and the complexity of some basic decision problems. Specifically, we show that the class of deterministic Data Walking Automata is closed under all Boolean operations, and that the class of non-deterministic Data Walking Automata has decidable emptiness, universality, and containment problems. We also prove that deterministic Data Walking Automata are strictly less expressive than non-deterministic Data Walking Automata, which in turn are captured by Class Memory Automata.

10 citations

Book ChapterDOI
16 Mar 2013
TL;DR: A decomposition of the property automaton is suggested into three smaller automata capturing the terminal, weak, and the remaining strong behaviors of theproperty, which can be used with any automata-based model checker.
Abstract: The automata-theoretic approach for model checking of linear-time temporal properties involves the emptiness check of a large Buchi automaton. Specialized emptiness-check algorithms have been proposed for the cases where the property is represented by a weak or terminal automaton. When the property automaton does not fall into these categories, a general emptiness check is required. This paper focuses on this class of properties. We refine previous approaches by classifying stronglyconnected components rather than automata, and suggest a decomposition of the property automaton into three smaller automata capturing the terminal, weak, and the remaining strong behaviors of the property. The three corresponding emptiness checks can be performed independently, using the most appropriate algorithm. Such a decomposition approach can be used with any automata-based model checker. We illustrate the interest of this new approach using explicit and symbolic LTL model checkers.

10 citations

Book ChapterDOI
16 May 2012
TL;DR: In this paper, a finite automata model for performing computations over an arbitrary structure is introduced, where the automaton processes sequences of elements in the structure and makes state transitions.
Abstract: We introduce a finite automata model for performing computations over an arbitrary structure $\mathcal S$ . The automaton processes sequences of elements in $\mathcal S$ . While processing the sequence, the automaton tests atomic relations, performs atomic operations of the structure $\mathcal S$ , and makes state transitions. In this setting, we study several problems such as closure properties, validation problem and emptiness problems. We investigate the dependence of deciding these problems on the underlying structures and the number of registers of our model of automata. Our investigation demonstrates that some of these properties are related to the existential first order fragments of the underlying structures.

10 citations


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