where nis the length of the solution. Let that solution be p=a
1
,...,a
n
, where
s
j+1
=γ(s
j
,a
j+1
)forj=0,...,n−1.Thenitiseasytoprovethattheplan
p
=a
1
,...,a
i−1
,a
k
,a
k+1
,...,a
n
isalsoasolution(seeExercise4.3).Thus,p
cannotbeashortest-lengthsolution.
4.3BackwardSearch
Planning canalso bedone usinga backwardsearch. The ideais tostart atthe goal
and applyinversesoftheplanningoperators toproducesubgoals,stopping ifwe
produce a setof subgoalssatisfied by theinitial state.The set of allstates that are
predecessors ...
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