a  ground  path;  it will  have  to  do  the  same  amount  of  search  as  if  ﬁnding  the  path  from  scratch  in  the  ground  graph. 
Algorithm WSPath implements weak and strong path reﬁnement. It ﬁrst tries to ﬁnd an abstract path σ . If this succeeds, 
then it passes the whole path σ to Reﬁne so the states along this path can be used as subgoals. If σ is weakly reﬁnable, 
then there is no need for Reﬁne to backtrack up to WSPath again, but there may still be a choice of ground subgoals in  f (ti )
for each state ti along σ . The amount of backtracking in this search will depend on how these choices are made. Finally, if 
σ is strongly reﬁnable, then there is not even any need to backtrack to the choose points within Reﬁne. It does not matter 
how we choose the subgoals in each  f (ti), there will always be a path to the next one.
A-framework-for-analysing-state-abstraction-metho_2022_Artificial-Intelligen