Section: New Results

Management of Large Distributed Systems

Analysis and synthesis of distributed systems

Participants : Éric Badouel, Thierry Jéron, Hervé Marchand, The Anh Pham

Control of Distributed Systems.

In [40], we have extended our examination of decentralized discrete-event-system architectures that use exclusive or (XOR) as the fusion rule to reach control decisions. A characterization of XOR inference-observable languages has been provided. Additionally, XOR observability is defined for languages that are not inference-observable but are distributed-observable.

Verification of distributed applications

In the context of IPL HAC-SPECIS, in collaboation with Martin Quinson (Myriads Inria project team) we are interested in the verification of real distributed applications.

In the conference paper [38] we explain the current status of the tool SimGridMC used for the verification of MPI applications. SimGridMC (also dubbed Mc SimGrid) is a stateful Model Checker for MPI applications. It is integrated to SimGrid, a framework mostly dedicated to predicting the performance of distributed applications. We describe the architecture of McSimGrid, and show how it copes with the state space explosion problem using Dynamic Partial Order Reduction and State Equality algorithms. As case studies we show how SimGrid can enforce safety and liveness properties for MPI applications, as well as global invariants over communication patterns.

Analysis of parameterized systems

Participants : Nathalie Bertrand, Éric Fabre, Blaise Genest, Matthieu Pichené, Ocan Sankur

Parameterized Verification of a time-synchronization protocol.

In [41], we consider distributed timed systems that implement leader-election protocols, which are at the heart of clock-synchronization protocols. We develop abstraction techniques for parameterized model checking of such protocols under arbitrary network topologies, where nodes have independently-evolving clocks. We apply our technique for model checking the root election part of the flooding time-synchronisation protocol (FTSP), and obtain improved results compared to previous work. We model-check the protocol for all topologies in which the distance to the node to be elected leader is bounded by a given parameter.

Controlling population models.

In [33], we introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. We study a synchronisation problem for such populations: no matter how individual agents react to the actions of the controller, the controller aims at driving all agents synchronously to a target state. The agents are naturally represented by a non-deterministic finite state automaton (NFA), the same for every agent, and the whole system is encoded as a 2-player game. The first player (Controller) chooses actions, and the second player (Agents) resolves non-determinism for each agent. The game with $m$ agents is called the $m$-population game. This gives rise to a parameterized control problem (where control refers to 2-player games), namely the population control problem: can Controller control the $m$-population game for all $m\in \mathbb{N}$, whatever Agents does?

In this work, we prove that the population control problem is decidable, and it is an EXPTIME-complete problem. As far as we know, this is one of the first results on parameterized control. Our algorithm, not based on cut-off techniques, produces winning strategies which are symbolic, that is, they do not need to count precisely how the population is spread between states. We also show that if there is no winning strategy, then there is a population size $M$ such that Controller wins the $m$-population game if, and only if, $m\le M$. Surprisingly, $M$ can be doubly-exponential in the number of states of the NFA, with tight upper and lower bounds.

Handling large biological systems.

This year, we propose to use approximated probabilistic distribution to handle large homogeneous populations of cells [39]. Beyond classical approximations, we propose to use the Chow-Liu tree representation, based on non-disjoint clusters of two variables. Our experiments show that our proposed approximation scheme is more accurate than existing ones to model probability distributions deriving from biopathways, while requiring a minimal complexity overhead.

To handle dynamics of a population of cells governed by biopathways, we develop coarse-grained abstractions of the biological pathways [21], and more precisely Dynamic Bayesian Networks (DBNs). We show that simulating a DBN is much faster than simulating the fine-grained model it abstracts, for comparable prediction performances.

We also explore the approximate inference problem of DBNs, that is, computing the probability distributions at every time point given the initial distribution at time 0. We evaluate several classical approximate inference algorithms for DBNs, and compare with a new method we propose, which consists in using the Chow-Liu tree approximation to represent distributions at each time step. It is very accurate, yet efficient according to experiments we report. We finally provide an error analysis of this approximate inference algorithm [39].