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.

A procedure for reachability analysis of rectangular automata

Abstract: We present a procedure for the reachability analysis of rectangular automata. These automata form a subclass of hybrid automata, with the main restriction being that all derivatives, guards, and invariants are defined by constant lower and upper bounds in each dimension. Our procedure exploits these restrictions to provide more efficient and robust computations. Unlike a procedure that we described in earlier work, the procedure presented here is exact in any dimension, up to the representation of rationals. If limited precision is available for storing rationals, the procedure can be easily modified to yield very close over-approximations. We use a two-tank example to demonstrate the effectiveness of our approach.

On the relationship between finite automata, finite monoids, and prefix codes.

Abstract: It is the aim of the present study to establish links between the structure of a given (finite) prefixcode and that of its syntactic monoid, using automata theory as a tool.

On asynchronous stochastic automata

Abstract: The paper deals with generalized stochastic automata (probabilistic sequential machines) which are able to print not only a single output but an output tape of arbitrary finite length each unit of time. Section 1 contains the basic definitions and some observations concerning the basic probabilities which are associated with each stochastic automaton. In section 2 the equivalence of situations and of automata is investigated. The principal result is the decidability of equivalence of finite situations of finite automata. Section 3, the main portion of the paper, is devoted to an investigation of the input-output relations, i.e., of the externally observable behavior, of stochastic automata. The existence of a so-called state family is shown to be a criterion for the generability of a stochastic operator within a stochastic automaton. The nonuniqueness of state families leads to a consideration of separability of stochastic operators, a property being, for generable stochastic operators, necessary and sufficient for the uniqueness of a state family. This property as well as a somewhat weaker property is characterized then. Some open problems are pointed out.

Büchi Store: an open repository of $$\omega $$ -automata

Abstract: We introduce Buchi Store, an open repository of Buchi automata and other types of $$\omega $$ -automata for model-checking practice, research, and education. The repository contains Buchi automata and their complements for common specification patterns and numerous temporal formulae. These automata are made as small as possible by various construction techniques in view of the fact that smaller automata are easier to understand and often help in speeding up the model-checking process. The repository is open, allowing the user to add automata that define new languages or are smaller than existing equivalent ones. Such a collection of Buchi automata is also useful as a benchmark for evaluating translation or complementation algorithms and as examples for studying Buchi automata and temporal logic. These apply analogously for other types of $$\omega $$ -automata, including deterministic Buchi and deterministic parity automata, which are also collected in the repository. In particular, the use of smaller deterministic parity automata as an intermediary helps reduce the complexity of automatic synthesis of reactive systems from temporal specifications.