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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TL;DR: In this paper, an automaton model specially tailored for working with modal $\mu$-calculus is presented, which can deal with arbitrary branching in a much simpler way as compare to the one proposed by Janin and Walukiewicz.
Abstract: $\mu$-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between $\mu$-Calculus and alternating tree automaton is used to solve the satisfiability and model checking problems by compiling the modal $\mu$-Calculus formula into an alternating tree automata. Thus advocating an automaton model specially tailored for working with modal $\mu$-Calculus. The advantage of the automaton model is its ability to deal with arbitrary branching in a much simpler way as compare to the one proposed by Janin and Walukiewicz. Both problems (i.e., model checking and satisfiability) are solved by reduction to the corresponding problems of alternating tree automata, namely to the acceptance and the non-emptiness problems, respectively. These problems, in turn, are solved using parity games where semantics of alternating tree automata is translated to a winning strategy in an appropriate parity game.
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01 Jan 2011
TL;DR: The object is to look at a few of results and techniques developed in the theory of automata and see what sorts of approaches have been applied to problems involving automata.
Abstract: 1. The title “theory of automata” has become somewhat passe because the problems of interest to people working in this area have changed, and therefore the subject has split into a number of different disciplines. Each of these disciplines is called by its own name, but many of the results and techniques developed in the theory of automata have turned out to be useful. Our object is to look at a few of these results and techniques and see what sorts of approaches have been applied to problems involving automata.
TL;DR: An original algorithm for transformation of finite automata to regular expressions is presented, based on effective graph algorithms and gives a transparent new proof of equivalence of regular expressions and infinite automata.
Abstract: An original algorithm for transformation of finite automata to regular expressions is presented. This algorithm is based on effective graph algorithms and gives a transparent new proof of equivalence of regular expressions and finite automata.
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TL;DR: It is shown that any factor of a finite automaton has chaotic limits but not vice versa, and as another simplicity criterion for dynamical systems the property of having chaotic limits (every point belongs to a set, whose $\omega-limit is chaotic).
Abstract: We conceive finite automata as dynamical systems on discontinuum and investigate their factors Factors of finite automata include many well-known simple dynamical systems, eg hyperbolic systems and systems with finite attractors In the quadratic family on the real interval, factors of finite automata include all systems with finite number of periodic points, as well as systems at the band-merging bifurcations On the other hand the system with a non-chaotic attractor, which occurs at the limit of the period doubling bifurcations (at the edge of chaos), is not of this class Next we propose as another simplicity criterion for dynamical systems the property of having chaotic limits (every point belongs to a set, whose $\omega$-limit is chaotic) We show that any factor of a finite automaton has chaotic limits but not vice versa
01 Feb 1987
TL;DR: It is proved that the necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographic Godel numbers of the strings belonging to each of the end-sets of M form an ultimately periodic set.
Abstract: In this paper we contribute some interesting results on the state space approach following the work of Lee [2], Yang and Huang [1].We prove that the necessary and sufficient condition for the state equation of a finite automaton M to have a rational solution is that the lexicographic Godel numbers of the strings belonging to each of the end-sets of M form an ultimately periodic set.A state space approach was proposed by Lee[2] as an alternative way to analyze finite automata. The approach is based on the transformation of a set of words into a formal power series over the field of integers modulo 2 and also obtaining a state equation in some linear space associated with the automaton. Some useful algorithms associated with the state space approach were discussed by Yang and Huang[1] along with a condition for the state equation to have a rational solution when the automaton has either 4 or 8 states.The question of existence of a rational solution of a state equation is certainly an interesting one and it is not difficult to see that the condition given by Yang and Huang [1] is by no means necessary even for automata with only 4 states.The main objective of our present work is to give the necessary and sufficient condition for the state equation of an automaton to have a rational solution and thus provide a complete answer to the question left open by Yang and Huang [1]. We also show that the condition obtained in [1] is a special case of our theorem.Furthermore, we discuss a practical method for determining whether the state equation of an automaton has a rational solution and also how to obtain the rational solution in case it exists.