(cid:4) and shrinking function 
= hi(G1) ⊗ G2 ⊗ . . . ⊗ Gp. Let V j be the variables deﬁning 
i−1. Then  fi is a transformation 
j ) = L(G j) = G(F ), so also in this case we can deﬁne the label relation 
(cid:10)
i ) as the identity relation. Finally, deﬁne τi = (cid:3) fi, Ri(cid:4), which is a transformation. We note that  fi can 
i , so τi is a VDA abstraction, and it is thus also M↑R(cid:14)C(cid:14).
3. Finally, suppose opi is a reduce labels operation. Let λi be the label reduction function for this step. For each G j =
⊗
= G
i have the same state sets, so we can deﬁne the transformation function  fi for this step as 
i−1). Deﬁne the transformation 
i−1, then it is 
, and it follows that τi is R↑ and C↑. Finally, opi is a reduce labels operation
A-framework-for-analysing-state-abstraction-metho_2022_Artificial-Intelligen