6.5 Discussion and Historical Remarks 137
The state resulting from the application of an allowed set can be defined as
in Section 6.3: γ (s, π
i
)=(s − effects
–
(π
i
)) ∪ effects
+
(π
i
). All propositions of
Section 6.2.3 can be rephrased for an allowed set and for a layered plan whose levels
are allowed sets by just replacing “any permutation” with “any allowed permutation”
(see Exercise 6.14).
In order to compute γ (s, π
i
) and to use such a set in the GP-Search procedure,
one does not need to produce an allowed permutation and to commit the plan
to it—one just needs to check its existence. We already noticed that an ordering
constraint “a before b” would be required whenever a allows b but b does not allow
a. It is easy to prove that a set is allowed if