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In the theory of discrete dynamical systems, a state space is the set of all possible configurations of a system. For example, a system in queueing theory defining the number of customers in a line would have state space {0, 1, 2, 3, ...}. State spaces can be either infinite or finite. An example of a finite state space is that of the toy problem Vacuum World, in which there are a limited set of configurations that the vacuum and dirt can be in. In the theory of discrete dynamical systems, a state space is the set of all possible configurations of a system. For example, a system in queueing theory defining the number of customers in a line would have state space {0, 1, 2, 3, ...}. State spaces can be either infinite or finite. An example of a finite state space is that of the toy problem Vacuum World, in which there are a limited set of configurations that the vacuum and dirt can be in. The states space is a directed graph where each possible state of a dynamical system is represented by a vertex, and there is a directed edge from a to b if and only if ƒ(a) = b where the function f defines the dynamical system. State spaces are useful in computer science as a simple model of machines. Formally, a state space can be defined as a tuple where:

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