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: A class of hybrid automata is introduced for which the reachability problem can be decided and the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first-order formulae over the reals, and it is shown that the techniques permit effective model checking for a nontrivial fragment of CTL.
Abstract: Hybrid systems are dynamical systems with the ability to describe mixed discrete-continuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning through a purely continuous-time modeling as with systems of differential equations, nor open to inferential processes commonly used for discrete state-transition systems such as finite state automata. A convenient and popular model, called hybrid automata, was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting. Intuitively, a hybrid automaton is simply a ''finite-state'' automaton with each state augmented by continuous variables, which evolve according to a set of well-defined continuous laws, each specified separately for each state. This article investigates both the notion of hybrid automaton and the model checking problem over such a structure. In particular, it relates first-order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions (x'@?f(x,t)) to a decidability problem for first-order formulaeover the reals. Furthermore, the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first-order formulaeover the reals. Despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite, we show that our techniques permit effective model checking for a nontrivial fragment of CTL.
20 citations
20 Sep 2006
TL;DR: Dynamical, computational, and problem solving capabilities of these automata networks are discussed through selected examples, and put into perspective with respect to current and future research.
Abstract: In this work standard lattice cellular automata and random Boolean networks are extended to a wider class of generalized automata networks having any graph topology as a support Dynamical, computational, and problem solving capabilities of these automata networks are then discussed through selected examples, and put into perspective with respect to current and future research.
20 citations
21 Jul 2008
TL;DR: This paper discusses recent developments relevant to NFAs related problems like, for example, simulation of and by several types of finite automata, minimization and approximation, size estimation of minimal NFAs, and state complexity of language operations.
Abstract: Nondeterministic finite automata (NFAs) were introduced in [67], where their equivalence to deterministic finite automata was shown. Over the last 50 years, a vast literature documenting the importance of finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss recent developments relevant to NFAs related problems like, for example, (i) simulation of and by several types of finite automata, (ii) minimization and approximation, (iii) size estimation of minimal NFAs, and (iv) state complexity of language operations. We thus come across descriptional and computational complexity issues of nondeterministic finite automata. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved.
20 citations
TL;DR: A set of regular expressions, called normalized expressions, are defined, such that every regular expression can be normalized in linear time, and it is proved that the equation automaton of a normalized expression is always smaller than its follow automaton.
Abstract: There exist two well-known quotients of the position automaton of a regular expression. The first one, called the equation automaton, was first introduced by Mirkin from the notion of prebase and has been redefined by Antimirov from the notion of partial derivative. The second one, due to Ilie and Yu and called the follow automaton, can be obtained by eliminating e-transitions in an e-NFA that is always smaller than the classical e-NFAs (Thompson, Sippu and Soisalon–Soininen). Ilie and Yu discussed the difficulty of succeeding in a theoretical comparison between the size of the follow automaton and the size of the equation automaton and concluded that it is very likely necessary to realize experimental studies. In this paper we solve the theoretical question, by first defining a set of regular expressions, called normalized expressions, such that every regular expression can be normalized in linear time, and proving then that the equation automaton of a normalized expression is always smaller than its follow automaton.
19 citations
TL;DR: It is shown that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.
Abstract: In this article we generalize concepts of the position automaton and ZPC-structure to the regular -expressions. We show that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.
19 citations