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Concurrency:  2021-2022



Schedule S1(CS&P)(3rd years)Computer Science and Philosophy

Schedule B1 (CS&P)Computer Science and Philosophy

Schedule S1(3rd years)Computer Science

Schedule B1Computer Science

Schedule S1(M&CS)(3rd years)Mathematics and Computer Science

Schedule B1(M&CS)Mathematics and Computer Science

MSc in Mathematics and Foundations of Computer Science



The lectures for this course will be live via MS Teams, via the live lectures channel here. Lectures will also be recorded and made available via the Computer Science Panopto site.
Computer networks, multiprocessors and parallel algorithms, though radically different, all provide examples of processes acting in parallel to achieve some goal. All benefit from the efficiency of concurrency yet require careful design to ensure that they function correctly. The concurrency course introduces the fundamental concepts of concurrency using the notation of Communicating Sequential Processes. By introducing communication, parallelism, deadlock, livelock, etc., it shows how CSP represents, and can be used to reason about, concurrent systems. Students are taught how to design communicating processes, how to construct realistic models of real systems, and how to write specifications that can be used to verify the correctness of the system models. One important feature of the module is its use of both algebraic laws and semantic models to reason about reactive and concurrent designs. Another is its use of FDR to animate models and verify that they meet their specifications.

Learning outcomes

At the end of the course the student should: 

  • understand some of the issues and difficulties involved in Concurrency;
  • be able to specify and model concuurent systems using CSP;
  • be able to reason about CSP models of systems using both algebraic laws and semantic models;
  • be able to analyse CSP models of systems using the model checker FDR.


  • Processes and observations of processes; point synchronisation, events, alphabets. Sequential processes: prefixing, choice, nondeterminism. Operational semantics; traces; algebraic laws.
  • Recursion. Fixed points as a means of explaining recursion; approximation, limits, least fixed points; guardedness and unique fixed points.
  • Concurrency. Hiding. Renaming.
  • Non-deterministic behaviours, refusals, failures.
  • Hiding and divergence, the failures-divergences model.
  • Specification and correctness.
  • Communication, buffers, sequential composition.


Deterministic processes: traces, operational semantics; prefixing, choice, concurrency and communication. Nondeterminism: failures and divergences; nondeterministic choice, hiding and interleaving. Advanced CSP operators. Refinement, specification and proof. Process algebra: equational and inequational reasoning.

Reading list

Lecture Notes: The lecture notes for this year's course appear online on the course materials page.

Course Text:


Background reading:

Overheads: This year's slides will appear on the course materials page over the course of the term.

Link to downloadable CSPM scripts from Roscoe's book:


Related research



Students are formally asked for feedback at the end of the course. Students can also submit feedback at any point here. Feedback received here will go to the Head of Academic Administration, and will be dealt with confidentially when being passed on further. All feedback is welcome.

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.