Formalizing problems as states, actions, and goals.
State space search is a foundational concept in AI for formalizing problem-solving. It provides a structured way to represent a problem, making it amenable to algorithmic solutions. The core idea is to define the problem in terms of a 'state space,' which is the set of all possible configurations the problem can be in. For a puzzle like the 8-puzzle, a state is any arrangement of the tiles. For a route-planning problem, a state is a specific city. The formulation requires several key components. First, the 'initial state' is where the search begins. Second, a set of 'actions' or 'operators' defines the valid moves that can be made to transition from one state to another. For the 8-puzzle, this would be sliding a tile up, down, left, or right into the empty space. Third, a 'transition model' specifies the resulting state after performing an action in a given state. Fourth, a 'goal test' is a function that determines whether a given state is a solution. Finally, a 'path cost' function assigns a numerical cost to a sequence of actions, which is often important for finding the best or most efficient solution, not just any solution. By defining a problem in these terms, we transform it into a graph search problem. Each state is a node in the graph, and each action is a directed edge connecting two nodes. The task then becomes finding a path from the initial state node to a goal state node, often while minimizing the total path cost. This abstraction is incredibly powerful because the same search algorithms can be applied to vastly different problems, as long as they can be framed within this state space model.