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

26 CHAPTER 2. THE LANGUAGE CCS
Definition 2.3 The collection P of CCS expressions is given by the following
grammar:
P, Q ::= K | α.P |
Pi | P | Q | P [f] | P \ L ,
where
• K is a process name in K;
• α is an action in Act;
i∈I
• I is a possibly infinite index set;
• f : Act → Act is a relabelling function satisfying the following constraints:
• L is a set of labels from L.
f(τ) = τ and
f(ā) = f(a) for each label a ;
We write 0 for an empty sum of processes, i.e.,
0 =
i∈∅
Pi ,
and P1 + P2 for a sum of two processes, i.e.,
P1 + P2 =
i∈{1,2}
Pi .
Moreover, we assume that the behaviour of each process constant K ∈ K is given
by a defining equation
K def
= P ,
where P ∈ P. As it was already made clear by the previous informal discussion,
the constant K may appear in P .
We sometimes write [b1/a1, . . . , bn/an], where n ≥ 1, ai, bi ∈ A for each i ∈
{1, . . . , n} and the ai are distinct channel names, for the relabelling [f], where f
is the relabelling function mapping each ai to bi, each ai to bi (i ∈ {1, . . . , n}) and
acting like the identity function on all of the other actions. For each label a, we
also often write \a in lieu of \{a}.
To avoid the use of too many parentheses in writing CCS expressions, we use
the convention that the operators have decreasing binding strength in the following