Discrete event systems : concepts and basic results
van Km Kees Hee, Pmp Paul Rambags · TU/e Research Portal · 1988
INo is the set of natural numbers including zero.IN} is the set of positive natural numbers.For S a set and T a binary relation over S, T* is the transitive closure of T. If A and B are sets, then A --> B denotes the set of all total functions from A to Band A f> B the set of all partial functions from A to B. For notational clarity we often write the function application f(x) by fx.We denote function restriction byt• For f a partial function from A to Band R ~ B, f1 R is the range-Most frameworks incorporate, in some form, the following notion of a system, here called basic system.A basic system consists of a state space S, a set L ~ S of initial states and a binary relation T over S, called the transition relation.If the system is in some state s E S it may move to a state t E S if and only if E T. Definitjon 1 Basic system.A basic system is a triple where S is a finite or countable set, L ~ Sand T ~ S x S. S is called the state space, L the set of initial states and T the transition relation.Elements of So :== {s E S 1.,3t E S : E T} are called terminal states