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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23 May 1998
TL;DR: A simple algorithm for deciding the nonemptiness of nondeterministic parity and Rabin tree automata is described, which runs in time O(n 2k+1 k!), where n is the number of states in the automaton and k is thenumber of pairs in the acceptance condition.
Abstract: Automata on in nite words and trees are used for speci cation and veri cation of nonterminating programs. The veri cation and the satis ability problems of speci cations can be reduced to the nonemptiness problem of such automata. In a weak automaton, the state space is partitioned into partially ordered sets, and the automaton can proceed from a certain set only to smaller sets. Reasoning about weak automata is easier than reasoning about automata with no restricted structure. In particular, the nonemptiness problem for weak alternating automata over a singleton alphabet can be solved in linear time. Known translations of alternating automata to weak alternating automata involve determinization, and therefore involve a double exponential blow-up. In this paper we describe simple and e cient translations, which circumvent the need for determinization, of parity and Rabin alternating word automata to weak alternating word automata. Beyond the independent interest of such translations, they give rise to a simple algorithm for deciding the nonemptiness of nondeterministic parity and Rabin tree automata. In particular, our algorithm for Rabin automata runs in time O(n 2k+1 k!), where n is the number of states in the automaton and k is the number of pairs in the acceptance condition. This improves the known O((nk) 3k ) bound for the problem.
142 citations
TL;DR: An automaton accepting L and built from the language M and if M is the set of minimal forbidden words of a single word ν, the automaton turns out to be the factor automaton of ν (the minimal automatonAccepting theSet of factors ofν), which yields a nontrivial upper bound on the number of minimal prohibitions of a word.
141 citations
10 Jul 1995
TL;DR: A time-abstract, phase-based methodology for checking if a given hybrid automaton has a finite bisimulation is advocated, which obtains new decidability results for hybrid systems as well as new, uniform proofs of known decidable results.
Abstract: The analysis, verification, and control of hybrid automata with finite bisimulations can be reduced to finite-state problems. We advocate a time-abstract, phase-based methodology for checking if a given hybrid automaton has a finite bisimulation. First, we factor the automaton into two components, a boolean automaton with a discrete dynamics on the finite state space \(\mathbb{B}\) m and a euclidean automaton with a continuous dynamics on the infinite state space ℝ n . Second, we investigate the phase portrait of the euclidean component. In this fashion, we obtain new decidability results for hybrid systems as well as new, uniform proofs of known decidability results.
141 citations
21 Jun 1994
TL;DR: A translation from timed Transition systems to event-recording automata is presented, which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors.
Abstract: We introduce the class of event- recording timed automata (ERA). An event-recording automaton contains, for every event a, a clock that records the time of the last occurrence of a. The class ERA is, on one hand, expressive enough to model (finite) timed transition systems and, on the other hand, determinizable and closed under all boolean operations. As a result, the language inclusion problem is decidable for event-recording automata. We present a translation from timed transition systems to event-recording automata, which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors.
134 citations
TL;DR: A simple theorem is proved that provides a lower bound on the size of nondeterministic finite automata which accept a given regular language.
133 citations