Brigitte Rozoy

Self-stabilizing counting in mobile sensor networks

Distributed computing has to adapt its techniques to mobile sensor networks and cope with constraints like small memory size or lack of computation power. In this paper we extend the results of Angluin et al (see [1,2,3,4]) by finding self-stabilizing algorithms to count the number of agents in the network. We focus on two different models of communication, with a fixed antenna or with pairwise interactions. In both models we decide if there exist algorithms (probabilistic, deterministic, with k-fair adversary) to solve the self-stabilizing counting problem.

Decidability of the Star Problem in A * × b *

We adress in this paper the decidability of the Star Problem in trace manoids: Let L be a recognizable trace language, is L∗ recognizable? We prove that this problem is decidable when the trace monoid is a direct product of free monoids A∗ × {b}∗. This result shows, for the first time and contrary to a possible intuition, that the Star Problem is of distinct nature than the Recognizability Problem: Let L be a rational trace language, is L recognizable?

Non-deterministic Population Protocols

In this paper we show that, in terms of generated output languages, non-deterministic population protocols are strictly more powerful than deterministic ones. Analyzing the reason for this negative result, we propose two slightly enhanced models, in which non-deterministic population protocols can be exactly simulated by deterministic ones. First, we consider a model in which interactions are not only between couples of agents, but also between triples and in which non-uniform initial states are allowed. We generalize this transformation and we prove a general property for a model with interactions between any number of agents. Second, we simulate any non-deterministic population protocol by a deterministic one in a model where a configuration can have an empty output.

Marrella : A tool to analyse the graph of states

Abstract: Traces and partial orders have been used as an approach to reduce time and memory in model-checking for concurrent programs. We show here that we can also make use of event structures and generalized traces: we extend algorithms for partial orders and traces by using event structure to generate reachability graphs; we gain for two reasons: first resulting algorithms are optimal and second a careful implementation spares memory.

Observing locally self-stabilization in a probabilistic way

A self-stabilizing algorithm cannot detect by itself that stabilization has been reached. For overcoming this drawback Lin and Simon introduced the notion of an external observer: a set of processes, one being located at each node, whose role is to detect stabilization. Furthermore, Beauquier, Pilard and Rozoy introduced the notion of a local observer: a single observing entity located at an unique node. This entity is not allowed to detect false stabilization, must eventually detect that stabilization is reached, and must not interfere with the observed algorithm. We introduce here the notion of probabilistic observer which realizes the conditions above only with probability 1. We show that computing the size of an anonymous ring with a synchronous self-stabilizing algorithm cannot be observed deterministically. We prove that some synchronous self-stabilizing solution to this problem can be observed probabilistically.

A method for the verification of a distributed and synchronized algorithm

In the model-checking context, the method used to detect stable properties is to construct the synchronized product of the input automata. The problem with such a method is the well-known state space explosion. We present a new algorithm that allows us to restrict this explosion, by constructing only the states necessary to check the stable properties. The basic idea is to forget the states that are not relevant to the verification. This is done by aggregating the concurrent transitions.