Memory lower bounds for deterministic self-stabilization

In the context of self-stabilization, a \emph{silent} algorithm guarantees that the register of every node does not change once the algorithm has stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that, for finding the centers of a graph, for electing a leader, or for constructing a spanning tree, every silent algorithm must use a memory of $\Omega(\log n)$ bits per register in $n$-node networks. Similarly, Korman et al. [Dist. Comp. '07] proved, using the notion of proof-labeling-scheme, that, for constructing a minimum-weight spanning trees (MST), every silent algorithm must use a memory of $\Omega(\log^2n)$ bits per register. It follows that requiring the algorithm to be silent has a cost in terms of memory space, while, in the context of self-stabilization, where every node constantly checks the states of its neighbors, the silence property can be of limited practical interest. In fact, it is known that relaxing this requirement results in algorithms with smaller space-complexity. In this paper, we are aiming at measuring how much gain in terms of memory can be expected by using arbitrary self-stabilizing algorithms, not necessarily silent. To our knowledge, the only known lower bound on the memory requirement for general algorithms, also established at the end of the 90's, is due to Beauquier et al.~[PODC '99] who proved that registers of constant size are not sufficient for leader election algorithms. We improve this result by establishing a tight lower bound of $\Theta(\log \Delta+\log \log n)$ bits per register for self-stabilizing algorithms solving $(\Delta+1)$-coloring or constructing a spanning tree in networks of maximum degree~$\Delta$. The lower bound $\Omega(\log \log n)$ bits per register also holds for leader election

Computing in the RAIN: a reliable array of independent nodes

The RAIN project is a research collaboration between Caltech and NASA-JPL on distributed computing and data-storage systems for future spaceborne missions. The goal of the project is to identify and develop key building blocks for reliable distributed systems built with inexpensive off-the-shelf components. The RAIN platform consists of a heterogeneous cluster of computing and/or storage nodes connected via multiple interfaces to networks configured in fault-tolerant topologies. The RAIN software components run in conjunction with operating system services and standard network protocols. Through software-implemented fault tolerance, the system tolerates multiple node, link, and switch failures, with no single point of failure. The RAIN-technology has been transferred to Rainfinity, a start-up company focusing on creating clustered solutions for improving the performance and availability of Internet data centers. In this paper, we describe the following contributions: 1) fault-tolerant interconnect topologies and communication protocols providing consistent error reporting of link failures, 2) fault management techniques based on group membership, and 3) data storage schemes based on computationally efficient error-control codes. We present several proof-of-concept applications: a highly-available video server, a highly-available Web server, and a distributed checkpointing system. Also, we describe a commercial product, Rainwall, built with the RAIN technology

Compact Deterministic Self-Stabilizing Leader Election: The Exponential Advantage of Being Talkative

This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the protocol is required to be \emph{silent} (i.e., when communication content remains fixed from some point in time during any execution), there exists a lower bound of Omega(\log n) bits of memory per node participating to the leader election (where n denotes the number of nodes in the system). This lower bound holds even in rings. We present a new deterministic (non-silent) self-stabilizing protocol for n-node rings that uses only O(\log\log n) memory bits per node, and stabilizes in O(n\log^2 n) rounds. Our protocol has several attractive features that make it suitable for practical purposes. First, the communication model fits with the model used by existing compilers for real networks. Second, the size of the ring (or any upper bound on this size) needs not to be known by any node. Third, the node identifiers can be of various sizes. Finally, no synchrony assumption, besides a weakly fair scheduler, is assumed. Therefore, our result shows that, perhaps surprisingly, trading silence for exponential improvement in term of memory space does not come at a high cost regarding stabilization time or minimal assumptions

Practical Distributed Control Synthesis

Classic distributed control problems have an interesting dichotomy: they are either trivial or undecidable. If we allow the controllers to fully synchronize, then synthesis is trivial. In this case, controllers can effectively act as a single controller with complete information, resulting in a trivial control problem. But when we eliminate communication and restrict the supervisors to locally available information, the problem becomes undecidable. In this paper we argue in favor of a middle way. Communication is, in most applications, expensive, and should hence be minimized. We therefore study a solution that tries to communicate only scarcely and, while allowing communication in order to make joint decision, favors local decisions over joint decisions that require communication.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

Verification of Multi-Agent Properties in Electronic Voting: A Case Study

Formal verification of multi-agent systems is hard, both theoretically and in practice. In particular, studies that use a single verification technique typically show limited efficiency, and allow to verify only toy examples. Here, we propose some new techniques and combine them with several recently developed ones to see what progress can be achieved for a real-life scenario. Namely, we use fixpoint approximation, domination-based strategy search, partial order reduction, and parallelization to verify heterogeneous scalable models of the Selene e-voting protocol. The experimental results show that the combination allows to verify requirements for much more sophisticated models than previously