Planning problems involve a *state space*
that captures all possible situations that could arise. The *state* could, for example, represent the position and orientation of a
robot, the locations of tiles in a puzzle, or the position and
velocity of a helicopter. Both discrete (finite, or countably
infinite) and continuous (uncountably infinite) state spaces will be
allowed. One recurring theme is that the state space is usually
represented *implicitly* by a planning algorithm. In most
applications, the size of the state space (in terms of number of
states or combinatorial complexity) is much too large to be explicitly
represented. Nevertheless, the definition of the state space is an
important component in the formulation of a planning problem and in
the design and analysis of algorithms that solve it.

Steven M LaValle
2020-08-14