So far we have discussed search from the point of view of a state space representation (i.e. state space search). We continue to hold to the state space view but we now consider a situation in which the previous methods `fall over'. Namely when there is an infinite number of operators that apply to some state or states. (We say that the branching rate is infinite: branching rate can be defined in terms of the number of branches at each node and some way of `averaging' the different value. The result is a crude measure of the ``bushiness'' of the search tree.)
If the branching rate is infinite we are in trouble. An example situation is the attempt to formalise how people get from Lancaster to Paris. We must allow operators for catching trains, planes and also for walking. Since the route from Lancaster to Paris is composed of a number of operator applications we have to bear in mind that there are an infinite number of routes to Paris. So how do we cope with this?
The intuition we now follow is that people do not solve problems without considering how `far' they are away from their goal. So if we can figure out whether a particuler move leads us nearer to our goal then we are doing well. Else we are not!