f (4) = 3, R(a, a) and τ = (cid:3) f , R(cid:4).

Example 17.
1. Let  S1 = {1, 2, 3, 4},  S2 = {1, 2, 3},  E1 = {(cid:3)1, 2, a(cid:4),(cid:3)3, 4, a(cid:4)} and  E2 = {(cid:3)1, 2, a(cid:4),(cid:3)2, 3, a(cid:4)}. Let  f (1) = 1,  f (2) = f (3) = 2, 
2. Same as (1) but add the arc (cid:3)1, 4, a(cid:4) to E1.
3. Let  S1 = {1, 2, 3, 4},  S2 = {1, 2},  E1 = {(cid:3)1, 2, a(cid:4)} and  E2 = {(cid:3)1, 2, a(cid:4)}. Let  f (1) = f (3) = 1,  f (2) = f (4) = 2,  R(a, a) and 
4. Same as (3) but add the arc (cid:3)3, 2, a(cid:4) to E1.
5. Let  S1 = S2 = {1, 2, 3},  E1 = {(cid:3)1, 2, a(cid:4),(cid:3)2, 3, a(cid:4)} and  E2 = {(cid:3)1, 3, a(cid:4)}. Let  f (1) = 1,  f (2) = 2,  f (3) = 3,  R(a, a) and  τ =
6. Let S1 = {1, 2}, S2 = {1, 2, 3, 4}, E1 = E2 = {(cid:3)1, 2, a(cid:4)}. Let  f (1) = {1, 3},  f (2) = {2, 4}, R(a, a) and τ = (cid:3) f , R(cid:4).

τ = (cid:3) f , R(cid:4).

(cid:3) f , R(cid:4).
A-framework-for-analysing-state-abstraction-metho_2022_Artificial-Intelligen