To find out whether the solutions steps can be ignored or undone. We have three classes of problems mentioned below :-
1. Ignorable : In which solution steps can be ignored (e.g., Theorem Proving).
Suppose we are trying to prove a mathematical theorem. First we proceed with proving a lemma that we think will be useful. Later we realize that it is not useful. So, Are we in serious trouble?. No, Still we can prove the theorem, only we need to ignore the first approach and start with another one to prove the theorem.
2. Recoverable : In which solution steps can be undone. (e.g., 8-Puzzle Problem).Suppose we have a 8-puzzle problem as shown in above figure. While attempting to solve the 8-puzzle problem, mistakenly we make a wrong move and realize that mistake. Now to correct our mistake we need to undo incorrect steps.
To undo incorrect steps the control mechanism for an 8-puzzle solver must keep track of the order in which steps are performed, so that we can backtrack to the initial state and start with some correct move.
3. Irrecoverable : In which solution steps cannot be undone. (e.g., Chess).Consider the problem of playing chess. Suppose playing chess program makes a wrong move and realize it after couple of moves. It cannot simply ignore the mistake. Neither it can be undone its move and start the game again. Here, once we make a move we never recover from that step. Only we can try to give the best of the current situation.
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