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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07 Jul 2008
TL;DR: A uniform framework for turning alternating tree automata into non-deterministic ones is presented and the first solution to (2) which does not make use of McNaughton's theorem (determinization) is presented.
Abstract: We present a uniform framework for (1) complementing Buchi automata, (2) turning Buchi automata into equivalent unambiguous Buchi automata, and (3) turning Buchi automata into equivalent deterministic automata. We present the first solution to (2) which does not make use of McNaughton's theorem (determinization) and an intuitive and conceptually simple solution to (3).
Our results are based on Muller and Schupp's procedure for turning alternating tree automata into non-deterministic ones.
74 citations
TL;DR: An infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automaton operating in realtime mode, whereas the size of the corresponding classical automata grows without bound.
73 citations
01 Jan 2001
TL;DR: In this paper, the authors give asymptotic estimates for the number of distinct languages and finite languages over a k-letter alphabet that are accepted by deterministic finite automata with n states.
Abstract: We give asymptotic estimates and some explicit computations for both the number of distinct languages and the number of distinct finite languages over a k-letter alphabet that are accepted by deterministic finite automata (resp. nondeterministic finite automata) with n states.
73 citations
TL;DR: In this article, a new geometric tool for analyzing groups of finite automata is introduced, which associates a square complex with a product of two trees if the automaton is bi-reversible.
Abstract: We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method we give examples of free groups and of Kazhdan groups which are generated by the different states of one finite (bi-reversible) automaton. We also reprove the theorem of Macedonska, Nekrashevych, Sushchansky, on the connection between bi-reversible automata and the commensurator of a regular tree.
73 citations
Journal Article•
72 citations