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

158 CHAPTER 7. MODELLING MUTUAL EXCLUSION ALGORITHMS
initial value of the variable k can be arbitrary. In order to ensure mutual exclusion,
each process Pi (i ∈ {1, 2}) executes the following algorithm, where we use j to
denote the index of the other process.
while true do
begin
‘noncritical section’;
bi := true;
k := j;
while (bj and k = j) do skip;
‘critical section’;
bi := false;
end
As many concurrent algorithms in the literature, Peterson’s mutual exclusion algorithm
is presented in pseudocode. Therefore one of our tasks, when modelling the
above algorithm, is to translate the pseudocode description of the behaviour of the
processes P1 and P2 into the model of labelled transition systems or into Milner’s
CCS. Moreover, the algorithm uses variables that are manipulated by the processes
P1 and P2. Variables are not part of CCS because, as discussed in Section 1.2,
process calculi like CCS are based on the message passing paradigm, and not on
shared variables. However, this is not a major problem. In fact, following the
message passing paradigm, we can view variables as processes that are willing to
communicate with other computing agents in their environment that need to read
and/or write them.
By way of example, let us consider how to represent the boolean variable b1 as
a process. This variable will be encoded as a process with two states, namely B1t
an B1f. The former state will describe the ‘behaviour’ of the variable b1 holding
the value true, and the latter the ‘behaviour’ of the variable b1 holding the value
false. No matter what its value is, the variable b1 can be read (yielding information
on its value to the reading process) or written (possibly changing the value held
by the variable). We need to describe these possibilities in CCS. To this end, we
shall assume that processes read and write variables by communicating with them
using suitable communication ports. For instance, a process wishing to read the
value true from variable b1 will try to synchronize with the process representing
that variable on a specific communication channel, say b1rt—the acronym means
‘read the value true from b1’. Similarly, a process wishing to write the value false
into variable b1 will try to synchronize with the process representing that variable
on the communication channel b1wf—‘write false into b1’.
Using these ideas, the behaviour of the process describing the variable b1 can
be represented by the following CCS expressions: