is not a homomorphism since (cid:3)1, 3, a(cid:4) ∈ E1 but (cid:3) f (1), f (3), a

(cid:10)(cid:4)  /∈ E2 for  any  (cid:2)

8.5.2.  Spurious states

We have earlier noted that the DPP criterion [92] is equivalent to P(cid:14). Since A↓ ⇒ PS↑ and PS↑ ⇒ P↑, we can alternatively 
deﬁne the DPP property as P↓A↓, instead of P(cid:14). Although P↓A↓ is a stronger criterion than P(cid:14) it means that we need not 
verify independently that P↑ holds if we already know that the heuristic is admissible, which is often the case.
A-framework-for-analysing-state-abstraction-metho_2022_Artificial-Intelligen