# State space

A **state space** is the set of all possible configurations of a system.[1] It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory.

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For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time[2] has an infinite discrete state space. The angular position of an undamped pendulum[3] is a continuous (and therefore infinite) state space.