Doubt in Simulation

Question

Here, initial state of K1xK2 is not in the pair with all initial states of K2 (namely Q3 and Q4). So how does the structure holds? I thought, for a structure to hold, every initial state of first structure should be in pair with every initial state of the second structure

Answer 1

Yes, every initial state of the first structure must have an initial state of the second one that simulates it. The first structure is here K1xK2, and the second structure is K2. So, we have to check whether for the initial states of K1xK2, i.e., the state P0Q0, there is an initial state of K2 in the relation, which is there, since we have (P0Q0,Q0) in the relation.

Comments

But P0Q0 has to simulate with all the initial states of K2 right? As all initial states of K2 must also be covered with all initial states of K1xK2, thus P0Q0 should be there with Q3 and Q4 initial states of K2 as well right? That is not the case here, so how does the structure hold?

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No, for every initial state of the first structure, there must be one initial state of the other structure.