State space search is a process used in computer science, including artificial intelligence (AI), to find a goal state with the desired property. A state space is a mathematical representation of a problem that defines all possible states that the problem can be in). In state space search, successive configurations or states of an instance are considered with the intention of finding a goal state with the desired property. Problems are often modeled as a state space, which is 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 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.
In state space search, a state space is formally represented as a tuple, in which:
- N 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
- f is the function that establishes which action is possible to perform in a certain state
- g is the function that returns the state reached performing action in state
- h is the cost of performing an action in state
State space search algorithms have a wide range of applications in various fields, including artificial intelligence, robotics, game playing, computer networks, operations research, bioinformatics, cryptography, and supply chain management. In artificial intelligence, state space search algorithms can be used to solve problems such as pathfinding, planning, and scheduling. Additionally, they can be employed to plan the motion of robots, determining the best sequence of actions to achieve a goal.
