This paper introduces a new probabilistic specification of reliable broadcast communication primitives, called Reliable Broadcast. This specification captures in a precise way the reliability of practical broadcast algorithms that, on the one hand, were devised with some form of reliability in mind but, on the other hand, are not considered reliable according to "traditional" reliability specifications.

In our DACE project [6], diverging requirements expressed through QoS are mainlyexplored bya varietyof different deliverysemantics implemented through different dissemination algorithms ranging from “classic ” Reliable Broadcast [18], to new and original algorithms, like the broadcast algorithm we introduce in [7], and which ensures reliable deliveryof events despite network failures. While striving for strong scalability, we have invested considerable effort in exploring probabilistic (gossip-based) algorithms. These appear to be more adequate in the field of large scale event dissemination than traditional strongly reliable approaches like [18]. Basically, probabilistic algorithms trade the strong reliability guarantees against very good scalability properties, yet still achieve a “pretty good degree of reliability ” [12]. Until now, most work on gossip-based algorithms considers broadcasting information to all participants in a system, paying little or no attention to individual and dynamic requirements, as typically encountered in contentbased dissemination. We present here Hierarchical Probabilistic Multicast (hpmcast [9]), a novel gossip-based algorithm which deals with the more complex case of multicasting an event to a subset of the system only. Requirements, such as limiting the consumption of local memoryresources byview and message buffering, as well as exploiting locality(the proximityof participants) and redundancy(commonalities in interests of these participants), are all addressed. Though hpmcast has been motivated byour specific context of TPS, it is general enough to be applied to any context in which a stronglyscalable primitive for event, message, or information dissemination is required. 1

this document is part of the workpackage 1 of the PEPITO project. This workpackage aims at defining formal models for aspects of distributed computation which are central for peer-to-peer systems. Transactions fall into this category and can help to design robust and fault-tolerant distributed programs. This final report contains our results concerning the axiomatization of the properties of transactions