• Segio Rajsbaum (IRIF, Université Paris Cité)
• Lelia Blin (IRIF, Université Paris Cité)

Distributed computing concerns designing and understanding algorithms for sets of independent computing units that have to communicate to coordinate their activities. The problem space of distributed computing is vast and it would be impossible to undertake an exhaustive study within a single course. Even a small-scale distributed system may expose an amazingly complex behavior that would make it very challenging to formally reason about. But we have to meet the challenge! Due to inherent limitations of centralized computing, all computing systems nowadays is becoming distributed, ranging from Internet-scale services to multiprocessors. Therefore, understanding the principles of distribution and concurrency is indispensable in all aspects of designing and engineering modern computing systems. The main challenge here is to balance correctness of the system's executions with its availability and efficiency, in the presence of possible misbehavior of the system components and the environment (such as faults and asynchrony).

This course discusses how to design distributed algorithms, reason about their correctness, and derive matching complexity bounds. The primary focus of the module is on understanding of the foundations of distributed computing. This course focuses on the models in which computing units communicate through a shared memory. The related course 2.18.1 deals with distributed algorithms for synchronous networks.

Lectures are given in English.

Tuesday, starting from ??/09/2026, ??-??, Bat. Sophie Germain, Room ??.

In a first part, we discuss semantics of concurrent programs to prove correctness or impossibility results

• Linearizability: definition and examples
• Proofs of linearizability, Locality theorem
• Progress conditions
• Asynchronous computability theorem for 2 processes
• Modeling n-process computability with simplicial complexes
• Impossibility of k-set agreement

In a second part, we discuss of the self stabilizing approach to tolerates failures

• Introduction to self-stabilization: faults, models, schedulers
• Dijkstra's Token ring algorithm
• Self-stabilizing algorithms for coloration
• Self-stabilizing Tree construction
• Unisson
• Self-stabilizing Leader election (mutual exclusion)

Final exam on ??, in room ??, starting at ??.

Duration: 3 hours.

All documents are allowed.

None, though some maturity in mathematical reasoning and algorithms is expected.

* Karine Altisen, Stéphane Devismes, Swan Dubois, Franck Petit: Introduction to Distributed Self-Stabilizing Algorithms. Synthesis Lectures on Distributed Computing Theory, Morgan & Claypool Publishers 2019

* Hagit Attiya and Jennifer Welch. Distributed Computing: Fundamentals, Simulations, and Advanced Topics. John Wiley and Sons, Inc.

* Shlomi Dolev: Self-Stabilization. MIT Press 2000, ISBN 0-262-04178-2

* R. Guerraoui and P. Kuznetsov. Algorithms for concurrent systems. PPUR, 2019

* Maurice Herlihy and Nir Shavit (Victor Luchangco, Michael Spear). The art of multiprocessor programming. Morgan Kaufmann 2008 (2020).

* M. Herlihy, D. Kozlov, S. Rajsbaum: Distributed Computing Through Combinatorial Topology Morgan Kaufman 2013.

* Michel Raynal: Concurrent Programming: Algorithms, Principles, and Foundation Springer

* Michel Raynal: Concurrent Programming Crash-prone Shared Memory Systems: A Few Theoretical NotionsMorgan & Claypool

* 2-11-2 Randomness in Complexity * 2-12-1 Techniques in Cryptography and Cryptanalysis * 2-13-2 Error correcting codes and applications to cryptography * 2-18-1 Distributed algorithms on networks * 2-18-2 Distributed algorithms on shared memory * 2-24-1 Algorithms and uncertainty * 2-29-1 Theory of practical graph algorithms * 2-34-1 Quantum information

* Lelia Blin Professeure],IRIF, CNRS, Université Paris Cité.

* Sergo Rajsbaum Directeur de Recherche, IRIF, CNRS, Université Paris Cité.