Abstraction reﬁnement refers to the following general technique. Suppose we want to ﬁnd a path from s to t in a ground 
graph  G1.  Then  we  map  s and  t to  their  corresponding  abstractions  f (s) and  f (t) in  an  abstract  graph  G2,  and  try  to 
ﬁnd a path σ = t0, (cid:2)1, t1, . . . , (cid:2)m, tm in G2, where t0 ∈ f (s) and tm ∈ f (t). There are two major techniques for reﬁning σ : 
label reﬁnement and  state reﬁnement.  Label  reﬁnement  proceeds  by  mapping  the  label  sequence  of  σ back  to  a  sequence 
λ = (cid:2)
(cid:10)
i , (cid:2)i) holds for all i. This new label sequence is usually not a valid plan in G1, so the reﬁnement 
process has to ﬁll in with additional labels until the result is a plan from  s to t that contains  λ as a subplan. Examples 
of  label  reﬁnement  appear  in  the  articles  by  Knoblock [65] and  Bacchus  and  Yang [3].  State  reﬁnement  instead  ignores
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