A state space representation refers to a formal model of all possible configurations (states) of a system or problem, along with the actions (or transitions) that move the system from one state to another.
Definition
A state space in AI is defined by:
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States: All possible situations the agent or system can be in.
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Initial State: The starting point of the problem.
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Goal State(s): The desired final condition(s).
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Operators/Actions: The rules that move from one state to another.
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Path Cost: (Optional) Cost associated with each transition.
Necessity of State Space in AI
- Foundation for Search Algorithms:
- Algorithms like BFS, DFS, A, etc.* work by exploring the state space.
- Problem Solving Framework:
- State space provides a structured way to represent and solve problems.
- Enables Planning:
- AI planning algorithms (used in robotics, games, etc.) rely on state transitions to find a valid sequence of actions.
- Helps in Modeling Real-World Problems:
- From puzzle-solving to autonomous navigation, state space helps describe complex problems systematically.
Example: 8-Puzzle Problem
Goal: Move tiles on a 3×3 board to reach the goal configuration.
Components
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State: A specific arrangement of the 8 numbered tiles and one empty space.
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Initial State: Starting configuration.
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Goal State:
1 2 3 4 5 6 7 8 _ -
Actions: Move the blank tile (up, down, left, right).
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Transition Model: Resulting state from applying an action.
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Path Cost: Each move has a cost (usually 1).
Visualization of State Transition:
Initial: Action: Move 8 left New State:
1 2 3 ------------------- 1 2 3
4 5 6 4 5 6
7 _ 8 7 8 _
Summary
In AI, state space representation is crucial because it:
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Defines how to represent problems clearly,
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Enables systematic exploration using search strategies,
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Forms the core logic behind many intelligent agents, including planners, robots, and game solvers.