**Understanding Problems**

Problem formulation is the process of defining and understanding the problem that needs to be solved. This involves identifying the initial state, goal state, actions available, and constraints within the problem domain.

**Problem Representation**

Once a problem is understood, it needs to be represented in a formal way that can be manipulated by an AI system. Common representations include state-space representation, problem-space representation, and goal formulation.

**State-Space Representation**

In state-space representation, the problem is represented as a set of states, with operators defining the transitions between states. This representation allows for the exploration of possible solution paths from the initial state to the goal state.

**Problem-Space Representation**

Problem-space representation involves defining the problem as a search through a space of possible problem-solving operations or transformations. This representation is often used in conjunction with state-space representation.

**Goal Formulation**

Goal formulation involves specifying the criteria or conditions that define the desired outcome of the problem-solving process. Goals can be explicit or implicit, and they guide the search for solutions.