Problem 2. Product Structures, Simulation and Bisimulation 15.02.2023

Question

Hello there, I just wanted to ask why didnt we split s1 and s4 in that question. In practice s1 goes to s5 while s4 goes to s2 which is a different group. Is this logic wrong, when I apply the other it was working.

Thank you in advance

Answer 1

We get the following diagrams:

    S0 --> {S2}
    |     
    S3 --> {S2}


    S1 --> {S0;S2;S5}
    |     
    S4 --> {S2;S3;S5}

So, it is clear that S0 is equivalent to S3. Also, S1->S0 is simulated by S4->S3, S1->S2 is simulated by S4->S2, and S1->S5 is simulated by S4->S5. Finally, S4->S2 is simulated by S1->S2, S4->S3 is simulated by S1->S0, and S4->S5 is simulated by S1->S5.

It seems that you ignored that S4 can also move to S5.

Comments

Oh,  I definitely missed that part now it is clear thank you