By Yoav Shoham
Synthetic Intelligence thoughts in Prolog
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Extra resources for Artificial Intelligence Techniques in Prolog
Best_first_search(arc,a,hf3,goal,L). 7. 4 suggests a few. However, even after optimization the program might run a long time, as nodes may be moved from the CLOSED list back into the OPEN list more t h a n once. Fortunately, there are cases in which we can avoid this. Notice t h a t in the sample run above, nodes were never removed from the CLOSED list; t h a t is, whenever a node was placed in CLOSED, an optimal p a t h to it had already been found. In general, a heuristic algorithm is called admissible if it finds not only a p a t h to a goal node an optimal path, t h a t is, a p a t h of minimal heuristic value.
Ab_max_children( [ Child | Children ], Alpha, Beta, MaxO, Max ) :ab_minimax( Child, Alpha, Beta, Value ), ( greater( Value, Beta ) - > Max = Beta % Beta pruning ; ab_max( Value, Alpha, AlphaO ), % Alpha update ab_max( Value, MaxO, Max1 ), ab_max_children( Children, AlphaO, Beta, Max1, Max ) ). ab_min_children( [ ], _, Min, Min ). abJTiin_children( [ Child | Children ], Alpha, Beta, MinO, Min ) :ab_minimax( Child, Alpha, Beta, Value ), ( greater( Alpha, Value ) - > Min = Alpha % Alpha pruning ; ab_min( Value, Beta, BetaO ), % Beta update ab_min( Value, MinO, Mini ), ab_min_children( Children, Alpha, BetaO, Mini, Min ) ).
It is possible to do better, by maintaining the O P E N and CLOSED sets other t h a n as lists. Also note t h a t the space complexity of this implementation is quadratic in the number of nodes, as all paths are stored explicitly; this complexity too can be reduced. 1 explores this topic further. Note also t h a t although the above program allows multiple solutions, it does not find multiple paths to any given node. 3. 5 Chapter 2. 3. We saw t h a t depthfirst search specializes it by selecting for exploration the latest node encountered.