Table of Contents
## Concurrency (24h, 3 ECTS)Course director: Emmanuel Haucourt ## Time schedule (8x3h)## Teacher for 2019-2020Emmanuel Haucourt ( professional web page) Final exam on Tuesday, the 3rd of March (second week of exams) 08h45 - 11h45. Due to strikes, I will not be able to reach Paris on the 10th of december 2019, the course is therefore cancelled. Due to strikes, I will not be able to reach Paris on the 17th of december 2019, the course is therefore cancelled. Cancelled courses have been moved to the 11th and 18th of February 2020. ## 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.
More advanced books: - McLane, S.
*Categories for the Working Mathematician (2nd ed.)*. Springer 1998. - Riehl, E.
*Category Theory in Context*. Dover 2016.
## 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: Final exam on Tuesday, the 3rd of March (second week of exams) 08h45 - 11h45. Due to strikes, I will not be able to reach Paris on the 10th of december 2019, the course is therefore cancelled. Due to strikes, I will not be able to reach Paris on the 17th of december 2019, the course is therefore cancelled. Cancelled courses have been moved to the 11th and 18th of February 2020. |