Many AI tasks can be framed as finding a sequence of actions that leads from a start state to a goal state. Search algorithms explore possible states and paths under resource limits.

A state space contains all possible configurations of a problem. A path cost function assigns a numerical cost to a solution path, often written as $g(n)$ for the cost to reach node $n$.

A* combines the actual cost so far $g(n)$ with a heuristic estimate $h(n)$ to form $f(n) = g(n) + h(n)$. When $h(n)$ is admissible, A* can guarantee optimal solutions.