A self-stabilizing system is one which can recover from transient faults in a nite number of steps. We present a theory for determining if a behavior speciication can be satissed with a self-stabilizing system and if not, then what the largest self-stabilizing subset and smallest self-stabilizing superset of the speciication is. The eeects of self-stabilizing behavior on the control of discrete...

A probabilistic self-stabilizing algorithm for a ring of identical processes is presented; the number of processes in the ring is odd, the processes operate synchronously, and communication is unidirectional in the ring. The normal function of the algorithm is to circulate a single token in the ring. If the initial state of the ring is abnormal, i.e. the number of tokens diiers from one, then e...

In this announcement, we report recent results where we address the open problem of snap-stabilization in messagepassing systems. (A full version of this paper is available as [3] at http://arxiv.org/abs/0802.1123.)

The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a small C1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stabilization condition by means of a boundary control, for ...

Running is an essential mode of human locomotion, during which ballistic aerial phases alternate with phases when a single foot contacts the ground. The spring-loaded inverted pendulum (SLIP) provides a starting point for modelling running, and generates ground reaction forces that resemble those of the centre of mass (CoM) of a human runner. Here, we show that while SLIP reproduces within-step...

We define and study an equivariant E-theory with respect to coactions of Hopf C-algebras; we prove the Baaj-Skandalis duality in this setting. We show that the corresponding equivariant KK-theory of Baaj and Skandalis enjoys an universal property. In the appendix, we look at the different ways of expressing equivariant stability for a functor, and prove an equivariant BrownGreen-Rieffel stabili...

The exit time and the exit location of a non-Markovian diffusion is analyzed. More particularly, we focus on the so-called self-stabilizing process. The question has been studied by Herrmann, Imkeller and Peithmann in [6] with results similar to those by Freidlin and Wentzell. We aim to provide the same results by a more intuitive approach and without reconstructing the proofs of Freidlin and W...