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I'm studying for my AI final exam, and I'm stuck in the state space representation. I understand initial and goal states, but what I don't understand is the state space and state transition function. Can someone explain what are they with example?

For example, one of the question was this on my previous exam:

Given

`k`

knights on a infinite (in all directions) chessboard and`k`

selected squares of the board. Our task to move the knights to these selected squares obeying the following simple rules:

- All knights move parallel, following their movement rule (L-shape jump)
- No knights can move to a square on which a knight stood anytime before
Give the state space of the problem, the starting and goal states, and the state transition function!