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 , in which: is the set of all possible states; is the set of possible actions, not related to a particular state but regarding all the state space; is the function that establishes which action is possible to perform in a certain state; is the function that returns the state reached performing action in state ; is the cost of performing an action in state . In many state spaces, is a constant, but this is not always true.
Examples of state-space search algorithms 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
See also State space State-space planning Branch and bound – Method for making state-space search more efficient by pruning subsets of it
References
Stuart J. Russell and Peter Norvig (1995). Artificial Intelligence: A Modern Approach. Prentice Hall.