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## 2.2 C**Altalt**

The CAltAlt planner uses the regression operator to generate children in an A* search. Regression terminates when search node expansion generates a belief state BS which is logically entailed by the initial belief state BSI . The plan is the sequence of actions regressed from BSG to obtain the belief state entailed by BSI .

For example, in the BTC problem, Figure 1, we have:
BS2 =Regress(BSG, DunkP1) = ¬clog ∧ (¬arm ∨ inP1).

The first clause is the execution formula and the second clause is the causation formula for the conditional effect of DunkP1 and ¬arm.

Regressing BS2 with Flush gives:
BS4 = Regress(BS2, Flush) = (¬arm ∨ inP1).

For BS4, the execution precondition of Flush is ⊤, the causation formula is **⊤ ∨ ¬**clog = ⊤, and
(¬arm ∨ inP1) comes by persistence of the causation formula.

Finally, regressing BS4 with DunkP2 gives:
BS9 = Regress(BS4, DunkP2) = ¬clog ∧ (¬arm ∨ inP1 ∨ inP2).

We terminate at BS9 because BSI |= BS9. The plan is DunkP2, Flush, DunkP1.

## 2.3 Progression

In progression we can handle both causative effects and observations, so in general, progressing the action a over the belief state BS generates the set of successor belief states B. The set of belief states B is empty when the action is not applicable to BS (BS 6|= ρ e(a)).

Progression of a belief state BS over an action a is best understood as the union of the result of applying a to each model of BS but we in fact implement it as BDD images, as in the MBP planner