Languages and Automata
We have seen how discrete-event systems (DES) differ from continuous-variable dynamic systems (CVDS) and why DES are not adequately modeled through differential or difference equations. Our first task, therefore, in studying DES is to develop appropriate models, which both adequately describe the behavior of these systems and provide a framework for analytical techniques to meet the goals of design, control, and performance evaluation.
When considering the state evolution of a DES, our first concern is with the sequence of states visited and the associated events causing these state transitions. To begin with, we will not concern ourselves with the issue of when the system enters a particular state or how long the system remains at that state. We will assume that the behavior of the DES is described in terms of event sequences of the form e 1 e 2 … n . A sequence of that form specifies the order in which various events occur over time, but it does not provide the time instants associated with the occurrence of these events. This is the untimed or logical level of abstraction discussed in Sect. 1.3.3 in Chap. 1, where the behavior of the system is modeled by a language. Consequently, our first objective in this chapter is to discuss language models of DES and present operations on languages that will be used extensively in this and the next chapters.
KeywordsRegular Expression Regular Language Parallel Composition Marked State Uncertain State
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∎Languages and Automata Theory
∎Automata and Related Modeling Formalisms
∎Some Other (Untimed) Modeling Formalisms for Discrete Event Systems
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