Table of Contents
## Concurrency (24h, 3 ECTS)Course director: Emmanuel Haucourt ## Time schedule (8x3h)## Teacher for 2019-2020Emmanuel Haucourt ( professional web page) ## GoalsStarting from a restriction of the language introduced by E. W. Dijkstra, we explain how directed algebraic topology can be applied to the study of concurrency. ## Plan of the course for 2019-2020- What kind of concurrency in this course?
- Restricted Dijkstra PV language
- Precubical sets as a generalization of graphs
- Control-flow graph, conservative programs, and precubical control flow
- Locally ordered spaces
- Directed realization of graphs and precubical sets
- Isothetic regions
- The fundamental category
- Seifert and van Kampen theorem for the fundamental category [optional]
- The category of components
- Factorization
- Some other topological models
## French and EnglishFrench. However, questions asked in english will be answered in english. ## MaterialSlides and (rather obsolete) lecture notes can be found here. ## Bibliography## Books- Fajstrup, L., Goubault, É., Haucourt, E., Mimram, S., and Raußen, M.
*Directed Algebraic Topology and Concurrency*. Springer 2016. - Brown, R.
*Topology and Groupoids*. BookSurge. 2006. - Higgins, P. J.
*Categories and Groupoids*. Van Nostrand-Reinhold 1975. - Hansen, P. B.
*The Origin of Concurrent Programming:*. Springer 2002. From Semaphores to Remote Procedure Calls
## Articles- Dijkstra, E. W.
*Cooperating Sequential Processes*. In Genuys, F. (ed.)
*Programming Languages: NATO Advanced Study Institute*. Academic Press 1968. - Fajstrup, L., Goubault, É., and Raußen, M.
*Algebraic Topology and Concurrency*. Theoretical Computer Science 357(1):241–278 2006. Presented at Mathematical Foundations of Computer Science in 1998 (London).
## Basic Category Theory- Awodey, S.
*Category Theory*. Clarendon Press. Oxford 2006. - Leinster, T.
*Basic Category Theory*. Cambridge University Press 2014. - Roman, S.
*An Introduction to the Language of Category theory*. Birkhäuser 2017.
## Related coursesSemantics (2.2), Concurrent algorithms (2.18.2). ## PrerequisitesIt is useful, though not strictly necessary, to have attended courses (similar to) 1-15 (Semantics) and 1-16 (Concurrency). ## ExamsTo be annouced ## Possible teachers
## Calendar 2019-2020
Second period: |