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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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Book ChapterDOI
02 Apr 2001
TL;DR: It is shown that the special structure of the acceptance condition of parity automata can be used in order to solve the nonemptiness problem directly, with a dynamic graph algorithm of complexity O((n + m) log k).
Abstract: Different types of nondeterministic automata on infinite words differ in their succinctness and in the complexity for their nonemptiness problem. A simple translation of a parity automaton to an equivalent Buchi automaton is quadratic: a parity automaton with n states, m transitions, and index k may result in a Buchi automaton of size O((n + m)k). The best known algorithm for the nonemptiness problem of parity automata goes through Buchi automata, leading to a complexity of O((n + m)k). In this paper we show that while the translation of parity automata to Buchi automata cannot be improved, the special structure of the acceptance condition of parity automata can be used in order to solve the nonemptiness problem directly, with a dynamic graph algorithm of complexity O((n + m) log k).

63 citations

Journal ArticleDOI
TL;DR: This work shifts the emphasis from the use of algebra automata as acceptors to the dynamics of algebras with outputs, and shows that the Nerode and Myhill approaches to state minimization and minimal dynamics can be carried through in the general case.
Abstract: Wright, Thatcher and Mezei have built on the observation of B\:uchi that finite automata may be considered to be monadic algebras, to study non-monadic algebras from the viewpoint of automata theory, and have generalized the usual studies of regular sets and context-free languages in this context. We continue this work, but shift the emphasis from the use of algebra automata as acceptors to the dynamics of algebras with outputs. We show that the Nerode and Myhill approaches to state minimization and minimal dynamics can be carried through in the general case. In Part I, we emphasize the interpretation of algebra automata as executing parallel programs. However, Eilenberg and Wright have shown that much of Wright, Thatcher and Mezei's work can be carried through in the context of categorical algebra, using the notion of algebraic theory introduced by Lawvere as a categorical explication of the notion of variety initiated by Birkhoff. Our results in Part I pave the way for the extension of this categorical framework to the treatment of algebra automata as dynamic systems in Part II [ Inform. Control 13, 346\2-370 (1968)].

63 citations

Journal ArticleDOI
TL;DR: In this paper, infinite periodic finitely generated groups are constructed, where the elements of the groups are mappings of a set of words in an alphabet X into itself induced by finite Mealy automata.
Abstract: New examples of infinite periodic finitely-generated groups are constructed. The elements of the groups are mappings of a set of words in an alphabet X into itself induced by finite Mealy automata. Estimates are given of the number of states and diagrams of the automata realizing the generating elements of the groups. There are three items in the literature cited.

63 citations

Journal ArticleDOI
TL;DR: The pumping lemma in automata theory based on quantum logic is established and the equivalence between the recognizabilty by the product and union of orthomodular lattice-valued automata is shown to be equivalent to the distributivity of meet over union in the truth-value set.
Abstract: We establish the pumping lemma in automata theory based on quantum logicunder certain conditions on implication, and discuss the recognizability by theproduct and union of orthomodular lattice-valued (quantum) automata. Inparticular, we show that the equivalence between the recognizabilty by the productof automata and the conjunction of the recognizabilities by the factor automatais equivalent to the distributivity of meet over union in the truth-value set.

63 citations

Journal ArticleDOI
TL;DR: In this paper, the membership problem is shown to be P-complete, provided a given automaton is deterministic, and each of the other problems is NP-complete for general finite-memory automata.

63 citations


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