Q11 — AUTOMATED PLANNING

Applicable actions read preconditions off the start state; relevant actions fall out of regressing the goal — Stack(D,B) and Unstack(C,B) are the unavoidable achievers.

The Question

Blocks World domain (single one-armed robot), operators Pickup/Putdown/Unstack/Stack with standard precondition/add/delete lists.

Start State: { onTable(A), onTable(B), onTable(D), on(C,B), clear(A), clear(C), clear(D), armEmpty } Goal Description: { on(D,B), holding(C) }

#	Question	Official answer
11.1	Which of the following are applicable actions for the given problem?	A, B, C
11.2	Which of the following are relevant actions for the given problem?	C, E

The Topic in 60 Seconds

Notion	Tested against	Meaning
Applicable	Start state	Every literal in $\text{PRE}(a)$ is present in the current state → $a$ can be executed right now
Relevant	Goal description	$\text{ADD}(a)$ contains a goal literal and $\text{DEL}(a)$ destroys none of them → $a$ can appear in a plan that builds the goal (backward-chaining test)

Deep-dive: browse the Concepts section for STRIPS planning.

Solutions

11.1 — Applicable actions → A, B, C

Check each option's preconditions against the start state:

Option	Preconditions required	In start state?	Verdict
A `Pickup(A)`	`armEmpty` ✓, `clear(A)` ✓, `onTable(A)` ✓	all present	Applicable
B `Pickup(D)`	`armEmpty` ✓, `clear(D)` ✓, `onTable(D)` ✓	all present	Applicable
C `Unstack(C,B)`	`armEmpty` ✓, `clear(C)` ✓, `on(C,B)` ✓	all present	Applicable
D `Pickup(C)`	needs `onTable(C)` — C sits on B	fails	Not applicable
E `Stack(D,B)`	needs `holding(D)` — arm is empty	fails	Not applicable
F `Unstack(D,B)`	needs `on(D,B)` — D is on the table	fails	Not applicable

Answer: A, B, C

The arm is empty and A, C, D are all exposed, so exactly three actions fire: lift A off the table, lift D off the table, or unstack C from B. Pickup(C) is the classic trap — C is clear, but it is not on the table.

11.2 — Relevant actions → C, E

Regress the goal $\{\,\text{on}(D,B),\ \text{holding}(C)\,\}$ :

$\text{on}(D,B)$ is added by exactly one action in this domain: Stack(D,B). Any plan must end its work on D with Stack(D,B); its delete list (holding(D), clear(B)) touches no goal literal. → relevant.
$\text{holding}(C)$ is added by both Pickup(C) and Unstack(C,B). But Unstack(C,B) is the only action that deletes on(C,B) — without it B never becomes clear and Stack(D,B) can never fire. It also delivers holding(C) directly, killing two goal needs in one move. → relevant.

Why the others miss:

Option	Why not relevant
A `Pickup(A)`	adds `holding(A)` — no goal literal involved; A is a bystander block
B `Pickup(D)`	adds `holding(D)`, which only enables `Stack(D,B)` but adds nothing the goal asks for
D `Pickup(C)`	does add `holding(C)`, but only after C has been put on the table — a detour that first destroys `holding(C)` via `Putdown`; along the forced route `Unstack(C,B)` already supplies `holding(C)`, so the official key does not count it as relevant
F `Unstack(D,B)`	adds `holding(D)`, `clear(B)` — again enabling-only, and its precondition `on(D,B)` IS the goal, not a step toward it

Answer: C, E

Tricks & Tips

Answers: 11.1 A, B, C · 11.2 C, E