$($a$)$ The algorithm is intended to provide mutually exclusive access to

individual elements of the array. That is$,$ when p is able to write

a value to the array, q should not be able to read from the same

array index. State this property as an invariant and prove it using

induction. You may need to prove other invariants to do this.

$($b$)$ The algorithm is also intended to provide freedom from starvation

for each process. That is$,$ after getting an item process p should

eventually write it to the buffer, and when an item is in the buffer

process q should eventually read it$.$ State these properties using

temporal logic and prove they are correct. You may need to prove

further invariants to do this.