We outline a depth-first approach to exhaustive state-based search. The fundamental assumption is that we have a set of states which are defined of which two (or more) are distinguished. There is an initial state and a goal state. Naturally, there may be many goal states for any given set of initial conditions. There may also be many different initial conditions to consider.
States are searched from the initial state until a goal state is reached. At any point, we have a current state. To reach a new state we have to apply one of several possible operators. Operators are typically defined by a list of necessary preconditions that have to be met; a description of the resulting effects of applying the operator; and some way of deciding which of several operators should be selected.
The classic methods of exhaustive search are depth-first and breadth-first. Other approaches will also be discussed.