Survey of Distributed Decision

We survey the recent distributed computing literature on checking whether a given distributed system configuration satisfies a given boolean predicate, i.e., whether the configuration is legal or illegal w.r.t. that predicate. We consider classical distributed computing environments, including mostly synchronous fault-free network computing (LOCAL and CONGEST models), but also asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile computing (FSYNC model)

Self-Stabilizing Token Distribution with Constant-Space for Trees

Self-stabilizing and silent distributed algorithms for token distribution in rooted tree networks are given. Initially, each process of a graph holds at most l tokens. Our goal is to distribute the tokens in the whole network so that every process holds exactly k tokens. In the initial configuration, the total number of tokens in the network may not be equal to nk where n is the number of processes in the network. The root process is given the ability to create a new token or remove a token from the network. We aim to minimize the convergence time, the number of token moves, and the space complexity. A self-stabilizing token distribution algorithm that converges within O(n l) asynchronous rounds and needs Theta(nh epsilon) redundant (or unnecessary) token moves is given, where epsilon = min(k,l-k) and h is the height of the tree network. Two novel ideas to reduce the number of redundant token moves are presented. One reduces the number of redundant token moves to O(nh) without any additional costs while the other reduces the number of redundant token moves to O(n), but increases the convergence time to O(nh l). All algorithms given have constant memory at each process and each link register

Self-Stabilization in the Distributed Systems of Finite State Machines

The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems

Weak vs. Self vs. Probabilistic Stabilization

Self-stabilization is a strong property that guarantees that a network always resume 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 self-stabilization. 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 algorthms are easier to design and prove than their (probabilistic) self-stabilizing counterparts

Engineering Resilient Collective Adaptive Systems by Self-Stabilisation

Collective adaptive systems are an emerging class of networked computational systems, particularly suited in application domains such as smart cities, complex sensor networks, and the Internet of Things. These systems tend to feature large scale, heterogeneity of communication model (including opportunistic peer-to-peer wireless interaction), and require inherent self-adaptiveness properties to address unforeseen changes in operating conditions. In this context, it is extremely difficult (if not seemingly intractable) to engineer reusable pieces of distributed behaviour so as to make them provably correct and smoothly composable. Building on the field calculus, a computational model (and associated toolchain) capturing the notion of aggregate network-level computation, we address this problem with an engineering methodology coupling formal theory and computer simulation. On the one hand, functional properties are addressed by identifying the largest-to-date field calculus fragment generating self-stabilising behaviour, guaranteed to eventually attain a correct and stable final state despite any transient perturbation in state or topology, and including highly reusable building blocks for information spreading, aggregation, and time evolution. On the other hand, dynamical properties are addressed by simulation, empirically evaluating the different performances that can be obtained by switching between implementations of building blocks with provably equivalent functional properties. Overall, our methodology sheds light on how to identify core building blocks of collective behaviour, and how to select implementations that improve system performance while leaving overall system function and resiliency properties unchanged.Comment: To appear on ACM Transactions on Modeling and Computer Simulatio

Self-Stabilizing Byzantine Resilient Topology Discovery and Message Delivery

Traditional Byzantine resilient algorithms use $2f + 1$ vertex disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. Distributed algorithms for topology discovery cope with a never ending task, dealing with frequent changes in the network topology and unpredictable transient faults. Therefore, algorithms for topology discovery should be self-stabilizing to ensure convergence of the topology information following any such unpredictable sequence of events. We present the first such algorithm that can cope with Byzantine nodes. Starting in an arbitrary global state, and in the presence of f Byzantine nodes, each node is eventually aware of all the other non-Byzantine nodes and their connecting communication links. Using the topology information, nodes can, for example, route messages across the network and deliver messages from one end user to another. We present the first deterministic, cryptographic-assumptions-free, self-stabilizing, Byzantine-resilient algorithms for network topology discovery and end-to-end message delivery. We also consider the task of r-neighborhood discovery for the case in which $r$ and the degree of nodes are bounded by constants. The use of r-neighborhood discovery facilitates polynomial time, communication and space solutions for the above tasks. The obtained algorithms can be used to authenticate parties, in particular during the establishment of private secrets, thus forming public key schemes that are resistant to man-in-the-middle attacks of the compromised Byzantine nodes. A polynomial and efficient end-to-end algorithm that is based on the established private secrets can be employed in between periodical re-establishments of the secrets