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We give a formal definition of what it means for a system to "tolerate" a class of "faults". The definition consists of two conditions: One, if a fault occurs when the system state is within a set of "legal" states, the resulting state is within some larger set and, if faults continue occurring, the system state remains within that larger set (Closure). And two, if faults stop occurring, the system eventually reaches a state within the legal set (Convergence). We demonstrate the applicability of our definition for specifying and verifying the fault-tolerance properties of a variety of digital and computer systems. Further, using the definition, we obtain a simple classification of fault-tolerant systems and discuss methods for their systematic design. as traditionally been studied in the context of specifi...

Abstract. Self-stabilizing message driven protocols are defined and discussed. The class weakexclusion that contains many natural tasks such as ℓ-exclusion and token-passing is defined, and it is shown that in any execution of any self-stabilizing protocol for a task in this class, the configuration size must grow at least in a logarithmic rate. This last lower bound is valid even if the system is supported by a time-out mechanism that prevents communication deadlocks. Then we present three self-stabilizing message driven protocols for token-passing. The rate of growth of configuration size for all three protocols matches the aforementioned lower bound. Our protocols are presented for two processor systems but can be easily adapted to rings of arbitrary size. Our results have an interesting interpretation in terms of automata theory.

Initial performance results and early experiences are reported for the Kendall Square Research multiprocessor. The basic architecture of the shared-memory multiprocessor is described, and computational and I/O performance is measured for both serial and parallel programs. Experiences in porting various applications are described. - v - 1. Introduction In September of 1991, a Kendall Square Research (KSR) multiprocessor was installed at Oak Ridge National Laboratory (ORNL). This report describes the results of this initial field test. The performance of the KSR shared-memory multiprocessor is compared with other shared-memory and distributed-memory multiprocessors, using synthetic benchmarks and real applications. Performance figures must be considered preliminary, since the KSR system was in its first field test. The KSR multiprocessor runs a modified version of OSF/1 (Mach). To the user, the KSR system appears like typical UNIX TM , but providing performance advantages similar to...

Those who cannot remember the past, are condemned to repeat it." (Philosopher George Santayana) In this paper we show that keeping track of history enables significant improvements in the communication complexity of dynamic networks protocols. We improve the communication complexity for solving any graph problem from \Theta(E) to \Theta(V ), thus achieving the lower bound. Moreover, O(V ) is also our amortized complexity of solving any function (not only graph functions) defined on the local inputs of the nodes. This proves, for the first time, that amortized communication complexity, i.e. incremental cost of adapting to a single topology change, can be smaller than the communication complexity of solving the problem from scratch. This also has a practical importance: in real networks the topology and the local inputs of the nodes change.

We propose a self stabilizing algorithm (protocol) for leader election in a tree graph. We show the correctness of the proposed algorithm by using a new technique involving induction. 1 Introduction In a distributed system the computing elements or nodes exchange information only by message passing. Every node has a set of local variables whose contents specify the local state of the node. The state of the entire system, called the global state, is the union of the local states of all the nodes in the system. Each node is allowed to have only a partial view of the global state, and this depends on the connectivity of the system and the propagation delay of different messages. Yet, the objective in a distributed system is to arrive at a desirable global final state (legitimate state), defined by some invariance relation on the global state. Systems that reach the legitimate state starting from any arbitrary (possibly illegitimate) state in a finite number of steps are called self-stabil...

Distributed computing is beginning to extend its scope to address problems relevant to a mobile environment (mobile computing). For the most part, current research efforts in mobile computing and ad hoc networking are implicitly aimed at mobile telephony and the emerging field of ubiquitous computing.

Many proposed self-stabilizing algorithms require an exponential number of moves before stabilizing on a global solution, including some rooting algorithms for tree networks [1, 2, 3]. These results are vastly improved upon in [6] with tree rooting algorithms that require only O(n³ + n² · c_h) moves, where n is the number of nodes in the network and c_h is the highest initial value of a variable. In the current paper, we describe a new set of tree rooting algorithms that brings the complexity down to O(n²) moves. This not only reduces the first term by an order of magnitude, but also reduces the second term by an unbounded factor. We further show a generic mapping that can be used to instantiate an efficient self-stabilizing tree algorithm from any traditional sequential tree algorithm that makes a single bottom-up pass through a rooted tree. The new generic mapping improves on the complexity of the technique presented in [8].

A randomized self-stabilizing algorithm A is an algorithm that, whatever the initial configuration is, reaches a set L of legal configurations in finite time with probability 1. The proof of convergence towards L is generally done by exhibiting a potential function ϕ, which measures the “vertical ” distance of any configuration to L, such that ϕ decreases with non-null probability at each step of A. We propose here a method, based on the notion of coupling, which makes use of a “horizontal” distance δ between any pair of configurations, such that δ decreases in expectation at each step of A. In contrast with classical methods, our coupling method does not require the knowledge of L. In addition to the proof of convergence, the method allows us to assess the convergence rate according to two different measures. Proofs produced by the method are often simpler or give better upper bounds than their classical counterparts, as examplified here on Herman’s mutual exclusion and Iterated Prisoner’s Dilemma algorithms in the case of cyclic graphs.

In recent years the labels “gossip ” and “gossip-based ” have been applied to an increasingly general class of algorithms, including approaches to information aggregation, overlay network management and clock synchronization. These algorithms are intuitively similar, irrespective of their purpose. Their distinctive features include relying on local information, being round-based and relatively simple, and having a bounded information transmission and processing complexity in each round. Our position is that this class can and should be significantly extended to involve algorithms from other disciplines that share the same orsimilar distinctive features, like certain parallel numerical algorithms, routing protocols, bio-inspired algorithms and cellular automata, to name but a few. Such a broader perspective would allow us to import knowledge and tools to design and understand gossip-based distributed systems, and we could also export accumulated knowledge to re-interpret some of the problems in other disciplines, such as vehicular traffic control. In this position paper we describe a number of areas that show parallels with gossip protocols. These example areas will hopefully serve as inspiration for future research. In addition, we believe that comparisons with other fields also helps clarify the definition of gossip protocols and represents a necessary first step towards an eventual formal definition. 1.