Parisian Master of Research in Computer Science
Master Parisien de Recherche en Informatique (MPRI)

COURSE 2.8.1

Non-Sequential Theory of Distributed Systems



The lectures will take place on Wednesday, 12:45 - 14:15, in Bat. Sophie Germain, Room 1004. The first lecture is on September 15, 2021.

The exam will take place on March 2, 12:45 - 14:15, in Bat. Sophie Germain, Room 1004.


The lecture shall cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over words, which provide a framework for modeling sequential systems. A distributed system, on the other hand, combines several (finite or recursive) processes, and will therefore be modeled as a collection of (finite or pushdown, respectively) automata. A crucial parameter of a distributed system is the kind of interaction that is allowed between processes. In this lecture, we focus on two standard communication paradigms: message passing and shared memory. In general, communication in a distributed system creates complex dependencies between events, which are hidden when using a sequential, operational semantics.

The approach taken in this lecture is based on a faithful preservation of the dependencies of concurrent events. That is, an execution of a system is modeled as a partial order, or graph, rather than a sequence of events. This has to be reflected in high-level languages for formulating requirements to be met by a distributed system. Actually, specifications for distributed systems are, by nature, non-sequential. They should be interpreted directly on the partial order underlying a system execution, rather than on an (arbitrary) linearization of it. It is worth mentioning that using specifications working on linearizations are often the reason for undecidability, as they may assume synchronization that actually cannot happen. We present classical specification formalisms such as monadic second-order (MSO) logic and temporal logic, interpreted over partial-orders or graphs, as well as (high-level) rational expressions. We compare the expressive power of automata and logic and give translations of specifications into automata (synthesis and realizability). Moreover, we consider the satisfiability (Is a given specification consistent?) and the model-checking problem (Does a given distributed system satisfy its specification?). For both problems, we present elementary techniques (based on tree interpretations and tree automata) that yield decision procedures with optimal complexity.

Outline of the course

Lecture Date Contents
1st 15/09/2021 Introduction and motivating examples
2nd 22/09/2021 Concurrent processes with data structures (CPDS); operational semantics of CPDS
3rd 29/09/2021 Graph semantics of CPDS
4th 06/10/2021 MSO logic; expressive power of MSO logic; from CPDS to MSO logic
5th 13/10/2021 MSO logic is strictly more expressive than CPDS
6th 20/10/2021 Exercises
7th 27/10/2021 Underapproximate verification
8th 03/11/2021 Special tree-width
9th 10/11/2021 Decomposition game; finite tree automata
24/11/2021 Mid-term exam
10th 08/12/2021 Proof of decidability of underapproximate verification
11th 05/01/2022 Propositional dynamic logic (syntax and semantics)
12th 12/01/2022 Expressive power of ICPDL
13th 19/01/2022 From PDL to CPDS
14th 26/01/2022 Model checking of ICPDL properties (1)
15th 02/02/2022 Model checking of ICPDL properties (2)
16th 23/02/2022 Exercises
02/03/2022 Exam

Lecture Notes


Basic knowledge in Automata, Logics, Complexity.

While not mandatory, it is useful to know the basics of verification. See for instance the level 1 course 1-22 Basics of verification which can also be taken during M2.


The lecture is given in English.

Related Courses

  • 2-3 Concurrency
  • 2-8-2 Foundations of real time and hybrid systems
  • 2-9-1 Mathematical foundations of the theory of infinite transition systems
  • 2-9-2 Algorithmic verification of programs
  • 2-16 Finite automata modelling
  • 2-20-1 Game theory techniques in computer science
  • 2-20-2 Mathematical foundations of automata theory


Universités partenaires Université Paris-Diderot
Université Paris-Saclay
ENS Cachan École polytechnique Télécom ParisTech
Établissements associés Université Pierre-et-Marie-Curie CNRS INRIA CEA