State Space
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In the theory of discrete dynamical systems, a state space is a directed graph (mathematics)|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: * N is a Set (mathematics)|set of states * A is a set of arcs connecting the states * S is a nonempty subset of N that contains start states * G is a nonempty subset of N that contains the goal states. A state space has some common properties: * complexity, where branching factor is important * structure of the space, see also graph theory: ** directionality of arcs ** tree ** rooted graph In a computer program, when the effective state space is small compared to all reachable state (computer science)|states, this is referred to as clumping....
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