Computation of the ND simulation according t the algorithm in the
lecture notes (note the definition of ND-simulation and the algorithm
for computing it must be written on the exam solution, also all
tuple deletions must be briefly justified).


R_0 (Note no final state in this example)

(t1,s1q1)
(t1,s1q2)
(t1,s2q1)
(t1,s2q2)

(t2,s1q1)
(t2,s1q2)
(t2,s2q1)
(t2,s2q2)

(t3,s1q1)
(t3,s1q2)
(t3,s2q1)
(t3,s2q2)

(t4,s1q1)
(t4,s1q2)
(t4,s2q1)
(t4,s2q2)


R_1

(t1,s1q1)
remove (t1,s1q2)  --- t1 can do c while s1q2 cannot
(t1,s2q1)
remove (t1,s2q2)  --- t1 can do c while s2q2 cannot

(t2,s1q1)
(t2,s1q2)
(t2,s2q1)
(t2,s2q2)

(t3,s1q1)
remove (t3,s1q2)  --- t3 can do c while s1q2 cannot
(t3,s2q1)
remove (t3,s2q2)  --- t3 can do c while s2q2 cannot

(t4,s1q1)
(t4,s1q2)
(t4,s2q1)
(t4,s2q2)


R_2

(t1,s1q1)
%removed (t1,s1q2)
(t1,s2q1)
%removed (t1,s2q2)

(t2,s1q1)
(t2,s1q2)  
(t2,s2q1)
(t2,s2q2)

(t3,s1q1)
%removed (t3,s1q2)
(t3,s2q1)
%removed (t3,s2q2)

(t4,s1q1)
(t4,s1q2)
(t4,s2q1)
(t4,s2q2)



At R_2 we cannot eliminate any tuple from the relation: i.e, R_2 is the
result of the algorithm (the greatest ND-simulation relation).



Now, on the basis of the greatest ND-simulation relation, we can
compute the output function of the orchestrator generator - see
lecture notes (note such output function mast be written on the exam
solution):

W(t1,s1q1,a) = {1,2}
W(t1,s2q1,a) = {2}

W(t1,s1q1,c) = {2}
W(t1,s2q1,c) = {2}

W(t2,s1q1,b) = {3}
W(t2,s1q2,b) = {2}
W(t2,s2q1,b) = {1,3}
W(t2,s2q2,b) = {2}

W(t3,s1q1,c) = {2}
W(t3,s2q1,c) = {2}

W(t4,s1q1,b) = {3}
W(t4,s1q2,b) = {2}
W(t4,s2q1,b) = {1,3}
W(t4,s2q2,b) = {2}

Any choice of the index, at each point in time, according to the above
function guarantees a composition.