Two methods dominate for exploiting state abstractions: abstraction reﬁnement and abstraction-based heuristics. Both ap-
proaches  will  be  brieﬂy  discussed  below.  In  both  cases,  it  is  also  common  to  build  hierarchies  of  abstractions  and  solve 
the problems top down, starting on the most abstract level; a method which dates back to Sacerdoti [78]. There are good 
reasons to consider hierarchical abstractions: Korf [68] showed that hierarchical abstraction can reduce the search space ex-
ponentially under ideal assumptions about the relationships between the abstraction layers. The abstraction reﬁnement and 
abstraction heuristic approaches are usually considered as quite different and unrelated. That is a very superﬁcial analysis, 
though:  both  approaches  are  ﬁrmly  based  on  properties  of  the  solutions  in  the  abstract  space,  so  some  connections  are
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