on unidirectional anonymous rings. This protocol does not required processor identifiers, no distinguished processor (i.e. all processors perform the same algorithm).

A new, self-stabilizing algorithm for electing a leader on a unidirectional ring of prime size is presented for the composite atomicity model with a centralized daemon. Its space complexity is optimal to within a small additive constant number of bits per processor, significantly improving previous self-stabilizing algorithms for this problem.

We consider Lehmann-Rabin's randomized solution to the well-known problem of the dining philosophers. Up to now, such an analysis has always required a "fairness" assumption on the scheduler: if a philosopher is continuously hungry then he must eventually be scheduled. In contrast here, we modify the algorithm in order to get rid of the fairness assumption. We claim that the spirit of the original algorithm is preserved. We prove that, for any (possibly unfair) scheduler, the modified algorithm converges: every computation reaches with probability 1 a configuration where some philosopher eats. Furthermore, we are now able to evaluate the expected time of convergence as a number of transitions. We show that, for some "malicious" scheduler, this expected time is at least exponential in the number N of philosophers.

Self-stabilization is a strong property which guarantees that a network always resume a correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic stabilization only gives probabilistic convergence to a correct behavior. Also, weak-stabilization only gives the possibility of convergence. In this paper, we investigate the relative power of weak, self, and probabilistic stabilization, with respect to the set of problems that can be solved. We formally prove that in that sense, weak stabilization is strictly stronger that selfstabilization. Also, we refine previous results on weak stabilization to prove that, for practical schedule instances, a deterministic weak-stabilizing protocol can be turned into a probabilistic self-stabilizing one. This latter result hints at more practical use of weak-stabilization, as such algorithms are easier to design and prove than their (probabilistic) selfstabilizing counterparts. 1.

We present a self-stabilizing token circulation protocol on unidirectional anonymous rings. This protocol does not required processor identifiers, no distinguished processor (i.e. all processors perform the same algorithm). The algorithm can deal with any kind of schedulings even unfair ones.

We study a special type of self-stabilizing algorithms composition : the cross-over composition

LRI/UMR 8623 CNRS, Universite Paris-Sud Batiment 490, F-91405 Orsay Cedex colette@lri.fr, www.lri.fr/colette/ We present a self-stabilizing token circulation protocol on unidirectional anonymous rings. The ring size is known by the processors. This protocol does not require processor identifiers, nor distinguished processor (i.e. all processors perform the same code).

model. A non deterministic distributed system is represented in the abstract model of transition systems. A distributed system is a tuple DS = (C; T ; I) where C is the set of all system configurations; T is a transition function of C to the set of C subsets; and I is a subset of the configuration set called the initial configurations. In a randomized distributed system, there is a probabilistic law on the output of a transition. A computation step is a pair of configurations (c i ; c j ) where c j is an output of a transition starting to c i . A computation e of DS is a sequence of consecutive computation steps e = (c 0 ; c 1 ); (c 1 ; c 2 ) : : :. where c 0 2 I.

Abstract. Adding Byzantine tolerance to large scale distributed systems is considered non-practical. The time, message and space requirements are very high. Recently, researches have investigated the broadcast problem in the presence of a fℓ-local Byzantine adversary. The local adversary cannot control more than fℓ neighbors of any given node. This paper proves sufficient conditions as to when the synchronous Byzantine consensus problem can be solved in the presence of a fℓ-local adversary. Moreover, we show that for a family of graphs, the Byzantine consensus problem can be solved using a relatively small number of messages, and with time complexity proportional to the diameter of the network. Specifically, for a family of bounded-degree graphs with logarithmic diameter, O(log n) time and O(n log n) messages. Furthermore, our proposed solution requires constant memory space at each node. This is the author’s copy of the paper. Please see

Abstract. We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin [22], augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size. 1