Table of Contents
## Concurrency (24h, 3 ECTS)Course director: Emmanuel Haucourt ## Academic year 2022 - 2023
## TeacherEmmanuel 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. ## French and EnglishFrench. However, questions asked in english will be answered in english. ## Plan of the Course and Material## SlidesA QUICK OVERVIEW OF CONCURRENCY THEORY PARALLEL AUTOMATA META LANGUAGE: Syntax, Control Flow Graph, Abstract Machine CONSERVATIVE PROGRAMS: Potential Functions, Discrete Models AN ALGEBRAIC TOPOLOGY TEASER: Categories, Topology, Functors, Connectedness METRIC SPACES: Functor terminology, Categories of metric spaces, Metric graphs LOCALLY ORDERED METRIC GRAPHS: Partially ordered spaces, Ordered atlases, Basic properties, Ordered atlas on metric graphs GEOMETRIC MODELS: Cartesian product, From discrete to geometric models, Examples, Geometric vs Discrete, The motivating theorem HOMOTOPY OF PATHS: Undirected case, Directed case, Relation to geometric models INDEPENDANCE: Syntactical independence, Model independence, Observational independence, Comparison ISOTHETIC REGIONS: Boolean structure, Additional operators FACTORING ISOTHETIC REGIONS: Free commutative monoids, Monoids of homogeneous languages, Homogeneous languages and isothetic regions FUNDAMENTAL CATEGORY: Abstract setting, Directed path functor, Natural congruences, Basic properties and computations CATEGORY OF COMPONENTS: Motivation, Loop-free categories, Systems of weak isomorphisms, Construction, Properties, Examples, Finite connected loop-free categories ## 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: - Mac Lane, S.
*Categories for the Working Mathematician (2nd ed.)*. Springer 1998. - Riehl, E.
*Category Theory in Context*. Dover 2016.
## Related coursesModels of programming languages: domains, categories, and games (2.2) Distributed algorithms on shared memory (2.18.2). ## ExamTBA
## Calendar and Time ScheduleTBA |