the speciﬁc weight function d, the distance function, which is deﬁned such that d(s, t) = 1 if there is an arc from s to t in E
and otherwise d(s, t) = ∞, i.e. d represents the unit cost assumption. When considering two STGs G1 and G2 simultaneously 
we index their corresponding c, d and w functions analogously, for instance, w1 is the weight function for G1.
We extend transformations with metric information, and we write τ = (cid:3) f , R, w1, w2(cid:4) when (cid:3) f , R(cid:4) is a transformation 
from G1 to G2 and  w1 and  w2 are the weight functions for G1 and G2, respectively. We could alternatively extend the 
STGs with weight functions. There is no difference in principle between the choices, but our approach allows for a simpler 
analysis. The cost functions c1 and c2 are implicitly deﬁned by w1 and w2. For instance, using the path length in the abstract
A-framework-for-analysing-state-abstraction-metho_2022_Artificial-Intelligen