Reactive Systems: Modelling, Specification and Verification - Cs.ioc.ee

160 CHAPTER 7. MODELLING MUTUAL EXCLUSION ALGORITHMS
we shall assume, for the sake of simplicity, that processes cannot fail or terminate
within the critical section. Under these assumptions, the initial behaviour of
process P1 can be described by the following CCS expression:
P1
def
= b1wt.kw2.P11 .
The above expression says that process P1 begins by writing true in variable b1 and
2 in variable k. Having done so, it will enter a new state that will be represented
by the constant P11. This new constant will intuitively describe the behaviour of
process P1 while it is executing the following line of pseudocode:
while (bj and k = j) do skip.
To simulate this ‘busy waiting’ behaviour, we expect that process P11 will
• read the value of the variables bj and k,
• loop back to P11 if bj is true and k is equal to 2, and
• move to a new state, say P12, otherwise. In state P12, we expect that process
P1 will enter and then exit the critical section.
The first thing to note here is that we need to make a decision as to the precise
semantics of the informal pseudocode expression
bj and k = j.
How is this boolean conjunction evaluated? Is it evaluated from left to right, or
from right to left? Assuming that it is evaluated from left to right, is the second
conjunct evaluated if the first turns out to yield false? Different answers to these
questions will produce different CCS processes. In what follows, we shall present
a CCS description for process P11 under the assumption that conjunctions are evaluated
from left to right, and that the second conjunct is not evaluated if the value
of the first is equal to false. Under these assumptions, we can write
P11
def
= b2rf.P12 + b2rt.(kr2.P11 + kr1.P12) .
Exercise 7.2 Would it have been a good idea to define P11 thus:
P11
def
= b2rf.P12 + b2rt.kr2.P11 + b2rt.kr1.P12 ?
Argue for your answer.