exercies 5 question 5: Quotient Structure

Question

My questions is

and using the tool I get this quotient structure

and my solution is

vars a,c,d;
init 0,3;
labels 0:; 1:; 2:c,d; 3:; 4:; 5:c,d;
transitions 0->1; 0->3; 1->2; 1->3; 2->3; 3->3;  5->3; 5->0;

I tried it to remove 4 but it is still wrong.

Answer 1

I'm a bit confused how S4 could be merged with any state as it has an edge to S5 which no other state has. Are you sure, you entered the task correctly to the tool? What's you solution when you do it manually?

Answer 2

When I am using the tool, I get another result which looks plausible to me. Did you use the following input (which is the given structure):

vars a,c,d;
init 0,3;
labels 0:; 1:; 2:c,d; 3:; 4:; 5:c,d;
transitions 0->1; 0->3; 1->2; 1->3; 2->3; 3->3; 3->4; 4->3; 4->5; 5->3; 5->0;

and did you compute K1≈K1?