State space search

State space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with the desired property.

Problems are often modelled as a state space, a set of states that a problem can be in. The set of states forms a graph where two states are connected if there is an operation that can be performed to transform the first state into the second.

State space search often differs from traditional computer science search methods because the state space is implicit: the typical state space graph is much too large to generate and store in memory. Instead, nodes are generated as they are explored, and typically discarded thereafter. A solution to a combinatorial search instance may consist of the goal state itself, or of a path from some initial state to the goal state.

Representation
In state space search, a state space is formally represented as a tuple $$ S: \langle S, A, Action(s), Result(s,a), Cost(s,a) \rangle $$, in which:
 * $$S$$ is the set of all possible states;
 * $$A$$ is the set of possible actions, not related to a particular state but regarding all the state space;
 * $$Action(s)$$ is the function that establishes which action is possible to perform in a certain state;
 * $$Result(s,a)$$ is the function that returns the state reached performing action $$a$$ in state $$s$$
 * $$Cost(s,a)$$ is the cost of performing an action $$a$$ in state $$s$$. In many state spaces a is a constant, but this is not always true.

Uninformed search
According to Poole and Mackworth, the following are uninformed state-space search methods, meaning that they do not have any prior information about the goal's location.
 * Traditional depth-first search
 * Breadth-first search
 * Iterative deepening
 * Lowest-cost-first search / Uniform-cost search (UCS)

Informed search
These methods take the goal's location in the form of a heuristic function. Poole and Mackworth cite the following examples as informed search algorithms:
 * Informed/Heuristic depth-first search
 * Greedy best-first search
 * A* search