Question

Answer the following questions explaining your reasoning briefly but precisely.

1. Why any node in OPEN with f(n) < f^*(n) (the cost of the optimal solution path) will eventually be selected for expansion by A*?
2. Is it true that all admissible heuristics are equal in the sense that A* will search the states in the same order no matter what the heuristic is?
3. Is Breadth-First search complete if the state space has infinite depth but a finite branching factor?
4. Does the fact that A* is ``optimally efficient'' mean that A* will never expand more nodes than any other algorithm?

Answer 1

If the node is open the A* algorithm v= w - 2 expanding the first node in the open list which minimizes the evaluation function

A* minly used for the optimal class path estimators.

if consistent admissible and heuristic estimators satisfying the equation h(n) less than equal to cost(a_n`) + h(n`) where the algorithm cost of cost(a_n`) which does not ever need to re expand automatically the node which is guranteed and hence the duplicates nodes are automatically directly deleted. on using the inconsistent & admissible heuristic estimator if the previous inequality does not hold true and still h(n) < h`(n)² for all the nodes n the algorithm still guarante still optimal solutions.

2) true

3)  the rationale for saying that BFS is complete while DFS is not (completeness is, after all, just a term that is defined somewhere) is that infinitely deep trees occur more frequently than trees with infinite branching factors (since having an infinite branching factor means that you have an infinite number of choices, which I believe is not common - games and simulations are usually discrete).

4) yes

f(n) = g(n) + h(n) where the h(n) is the heuristic function y any node in OPEN with f(n) < f^*(n) (the cost of the optimal solution path) will eventually be selected for expansion by A*?