State-space search

Template:Short description 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 $S:⟨S,A,\mathrm{Action}(s),\mathrm{Result}(s,a),\mathrm{Cost}(s,a)⟩$, 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;
• $\mathrm{Action}(s)$ is the function that establishes which action is possible to perform in a certain state;
• $\mathrm{Result}(s,a)$ is the function that returns the state reached performing action $a$ in state $s$;
• $\mathrm{Cost}(s,a)$ 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.

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.

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