Department of Computer Science and Technology

Course pages 2019–20


Unit: Topics in Concurrency

This course is only taken by Part II 75% students.

Lecturer: Professor G. Winskel

No. of lectures: 16

Suggested hours of supervisions: 3

Prerequisite course: Semantics of Programming Languages (specifically, an idea of operational semantics and how to reason from it)

Capacity: no restrictions


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 concurrent systems. Students will be assessed by a one-hour test at the end of the course.


  • Simple parallelism and nondeterminism. Dijkstra’s guarded commands. Communication by shared variables: A language of parallel commands. [1 lecture]

  • Communicating processes. Milner’s Calculus of Communicating Processes (CCS). Pure CCS. Labelled-transition-system semantics. Bisimulation equivalence. Equational consequences and examples. [3 lectures]

  • Specification and model-checking. The modal mu-calculus. Its relation with Temporal Logic, CTL. Model checking the modal mu-calculus. Bisimulation checking. Examples. [3 lectures]

  • Introduction to Petri nets. Petri nets, basic definitions and concepts. Petri-net semantics of CCS. [1 lecture]

  • Cryptographic protocols. Cryptographic protocols informally. A language for cryptographic protocols. Its Petri-net semantics. Properties of cryptographic protocols: secrecy, authentication. Examples with proofs of correctness. [2 lectures]

  • Mobile computation. An introduction to process languages with process passing and name generation. [2 lectures]


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 computation;

  • 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 mobile computation.

Recommended reading

Comprehensive notes will be provided.

Further reading:

* Aceto, L., Ingolfsdottir, A., Larsen, K.G. & Srba, J. (2007). Reactive systems: modelling, specification and verification. Cambridge University Press.
Milner, R. (1989). Communication and concurrency. Prentice Hall.
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.