Problem 1 (30 points): Consider the two transition systems below that both model a beverage
vending machine.
pay
?
pay
?
?
soda
select
beer
select?
soda
beer
select?
?
The left transition system models a beverage machine that after insertion of a coin
nondeterministically chooses to either provide soda or beer. The right one, however, has two
selection buttons (one for each beverage), and after insertion of a coin, nondeterministically blocks
one of the buttons. In either case, the user has no control over the beverage obtained—the choice
of beverage is under full control of the vending machine. Let AP = {pay, soda, beer},
a. Prove that the two systems are trace equivalence.
b. Give an example of a finite execution fragment of these transition systems where soda
appears two times and beer appear one time.
c. Give an example of a finite execution fragment of these transition systems where each
proposition appears at least three times.
d. Give an example of a trace of these transition systems where each proposition appears
at least two times.
