Prerequisite course: Semantics of Programming Languages (specifically, an idea of operational semantics and how to reason from it)
The aim of this course is to introduce fundamental concepts and
techniques in the theory of concurrent processes. It will provide
languages, models, logics and methods to formalise and reason about
Simple parallelism and nondeterminism.
Dijkstra's guarded commands. Communication by shared variables:
A language of parallel commands.
Milner's Calculus of Communicating Processes (CCS).
Pure CCS. Labelled-transition-system semantics.
Bisimulation equivalence. Equational consequences and examples.
Specification and model-checking.
The modal mu-calculus. Its relation with Temporal Logic, CTL.
Model checking the modal mu-calculus. Bisimulation checking.
Introduction to Petri nets.
Petri nets, basic definitions and concepts.
Petri-net semantics of CCS.
Cryptographic protocols informally. A language for cryptographic
protocols. Its Petri-net semantics. Properties of cryptographic
protocols: secrecy, authentication. Examples with proofs of
An introduction to process languages with process passing and name
generation. The Pi-Calculus and Ambient Calculus briefly.
At the end of the course students should
know the basic theory of concurrent processes:
non-deterministic and parallel commands, the process language CCS, its
transition-system semantics, bisimulation, the modal mu-calculus,
Petri nets, languages for cryptographic protocols and mobile
be able to
formalise and to some extent analyse concurrent processes: establish
bisimulation or its absence in simple cases, express and establish
simple properties of transition systems in the modal mu-calculus,
argue with respect to a process language semantics for secrecy or
authentication properties of a small cryptographic protocol, formalise
Comprehensive notes will be provided.
* Milner, R. (1999). Communicating and mobile systems: the Pi-calculus. Cambridge University Press.
Winskel, G. (1993). The formal semantics of programming languages, an introduction. MIT Press.
Milner, R. (1989). Communication and concurrency. Prentice-Hall.