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State space search

Problems are often modelled as a state space, a setofstates 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[edit]

In state space search, a state space is formally represented as a tuple ${\displaystyle S:\langle S,A,Action($s),Result(s,a),Cost(s,a)\rangle } , in which:

• ${\displaystyle S}$ is the set of all possible states;
• ${\displaystyle A}$ is the set of possible actions, not related to a particular state but regarding all the state space;
• ${\displaystyle Action($s)} is the function that establishes which action is possible to perform in a certain state;
• ${\displaystyle Result(s,a)}$ is the function that returns the state reached performing action ${\displaystyle a}$ in state ${\displaystyle s}$
• ${\displaystyle Cost(s,a)}$ is the cost of performing an action ${\displaystyle a}$ in state ${\displaystyle s}$. In many state spaces a is a constant, but this is not always true.

Examples of state-space search algorithms[edit]

Uninformed search[edit]

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.^[1]

• Traditional depth-first search
• Breadth-first search
• Iterative deepening
• Lowest-cost-first search / Uniform-cost search (UCS)

Informed search[edit]

These methods take the goal's location in the form of a heuristic function.^[2] Poole and Mackworth cite the following examples as informed search algorithms:

• Informed/Heuristic depth-first search
• Greedy best-first search
• A* search

See also[edit]

• State space
• State space planning
• Branch and bound - a method for making state-space search more efficient by pruning subsets of it.

References[edit]

• Stuart J. Russell and Peter Norvig (1995). Artificial Intelligence: A Modern Approach. Prentice Hall.

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