So far we have described lots of search algorithms, but not how they are used in solving problems. In general, search techniques are used to find a sequence of actions that will get us from some initial state to some goal state or states. The actions may be physical actions (such as move from town A to town B, or put block C on the table) or may be more abstract actions, like theorem proving steps (we may be searching for a sequence of steps that will allow us to prove X from the set of facts S).
There are two basic approaches to using search in problem solving. In the first (state-space search) a node in the search tree is a state of the world. Successor nodes in the search tree will be possible new states. In the second (problem reduction) a node in the search tree is a goal (or set of goals) to be satisfy. Successor nodes will be the different subgoals that can be used to satisfy that goal. These two approaches will be discussed in turn (though we'll emphasise state-space search).