Table of Contents
## Concurrency (24h, 3 ECTS)Course director: Emmanuel Haucourt ## Academic year 2023 - 2024
## TeacherEmmanuel Haucourt (professional web page) ## GoalsIn view of studying concurrency in a continuous setting, we introduce topology, geometry, and order theory needed to define a semantics of a restriction of the language introduced by E. W. Dijkstra. ## 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 MODELS: Cartesian product, From discrete to geometric models, Examples, Geometric vs Discrete, The motivating theorem, From geometric to smooth models 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). - Haucourt, E.
*The geometry of conservative programs*. Mathematical Structures in Computer Science, 2018.
## 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). ## Exam8 march 2024, 8h45 - 11h45, Sophie Germain building, room 1002.
## Calendar and Time Schedule8h45 - 11h45, Sophie Germain building, room 1002 8, 15 december 2023 12, 19, 26 january 2024 2, 9, 16 february 2024 |