**The AO* ALGORITHM**

**The problem reduction algorithm we just described is a simplification of an algorithm described in Martelli and Montanari, Martelli and Montanari and Nilson. Nilsson calls it the AO* algorithm , the name we assume.**

**1. Place the start node s on open.**

**2. Using the search tree constructed thus far, compute the most promising solution tree T**

**3. Select a node n that is both on open and a part of T. Remove n from open and place it on closed.**

**4. If n is a terminal goal node, label n as solved. If the solution of n results in any of n’s ancestors being solved, label all the ancestors as solved. If the start node s is solved, exit with success where T is the solution tree. Remove from open all nodes with a solved ancestor.**

**5. If n is not a solvable node (operators cannot be applied), label n as unsolvable. If the start node is labeled as unsolvable, exit with failure. If any of n’s ancestors become unsolvable because n is, label them unsolvable as well. Remove from open all nodes with unsolvable ancestors.**

**6. Otherwise, expand node n generating all of its successors. For each such successor node that contains more than one sub problem, generate their successors to give individual sub problems. Attach to each newly generated node a back pointer to its predecessor. Compute the cost estimate h* for each newly generated node and place all such nodes that do not yet have descendents on open. Next, recomputed the values of h* at n and each ancestor of n.**

**7. Return to step 2.**

any example of A* nd AO* please

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