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

2.1. SOME CCS PROCESS CONSTRUCTIONS 17
processes
CHM def
= coin.choc.CHM
DFM def
= coin.figs.DFM
CRM def
= coin.crisps.CRM .
Note, however, that all of these vending machines follow a common behavioural
pattern, and may be seen as specific instances of a generic vending machine that
receives a coin as input, dispenses an item and restarts, namely the process
VM def
= coin.item.VM .
All of the aforementioned specific vending machines may be obtained as appropriate
‘renamings’ of VM. For example,
CHM def
= VM[choc/item] ,
where VM[choc/item] is a process that behaves like VM, but outputs chocolate
whenever VM dispenses the generic item. In general,
If P is a process and f is a function from labels to labels satisfying
certain requirements that will be made precise in Section 2.2, then
P [f] is a process.
By introducing the relabelling operation, we have completed our informal tour
of the operations offered by the language CCS for the description of process behaviours.
We hope that this informal introduction has given our readers a feeling
for the language, and that our readers will agree with us that CCS is indeed a
language based upon very few operations with an intuitively clear semantic interpretation.
In passing, we have also hinted at the fact that CCS processes may be
seen as defining automata which describe their behaviour—see Exercise 2.3. We
shall now expand a little on the connection between CCS expressions and the automata
describing their behaviour. The presentation will again be informal, as we
plan to highlight the main ideas underlying this connection rather than to focus immediately
on the technicalities. The formal connection between CCS expressions
and labelled transition systems will be presented in Section 2.2 using the tools of
Structural Operational Semantics (Plotkin, 1981; Plotkin, 2004b).
2.1.1 The behaviour of processes
The key idea underlying the semantics of CCS is that a process passes through
states during its execution; processes change their state by performing actions. For