We initiate a study of bounded clock synchronization under a more severe fault model than that proposed by Lamport and Melliar-Smith [LM-85]. Realistic aspects of the problem of synchronizing clocks in the presence of faults are considered. One aspect is that clock synchronization is an on-going task, thus the assumption that in any period of the execution at least two thirds of the processors are nonfaulty is too optimistic. To cope with this reality we suggest self-stabilizing protocols that stabilize in any (long enough) period in which less than a third of the processors are faulty. Another aspect is that the clock value is bounded. A single transient fault may cause the clock to reach the upper bound. Therefore we suggest a bounded clock that wraps around when appropriate. We present two randomized self-stabilizing protocols for synchronizing bounded clocks in the presence of Byzantine processor failures. The rst protocol assumes that processors have a common pulse, while the second protocol does not. A new type of distributed counter based on the Chinese remainder theorem is used as part of the rst protocol. 1

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.

This paper studies self-stabilization in networks of anonymous, asynchronously interacting nodes where the size of the network is unknown. Constant-space protocols are given for Dijkstra-style round-robin token circulation, leader election in rings, 2-hop coloring in degree-bounded graphs, and establishing consistent global orientation in an undirected ring. A protocol to construct a spanning tree in regular graphs using O(log D) memory is also given, where D is the diameter of the graph. A general method for eliminating nondeterministic transitions from the self-stabilizing implementation of a large family of behaviors is used to simplify the constructions, and general conditions under which protocol composition preserves behavior are used in proving their correctness.

. A self-stabilizing system is a distributed system which can tolerate any number and any type of faults in the history. After the last fault occurs the system starts to converge to a legitimate behavior. The self-stabilization property is very useful for systems in which processors may malfunction for a while and then recover. When there is a long enough period during which no processor malfunctions the system stabilizes. Dynamic systems are systems in which communication links and processors may fail and recover during normal operation. Such failures could cause partitioning of the system communication graph. The application of self-stabilizing protocols to dynamic systems is natural. Following the last topology change each connected component of the system stabilizes independently. We present time optimal self-stabilizing dynamic protocols for a variety of tasks including: routing, leader election and topology update. The protocol for each of those tasks stabilizes in \Theta(d) ti...

A distributed algorithm is self-stabilizing if it can be started from any possible global state. Once started, the algorithm converges to a consistent global state by itself. This paper presents a distributed self-stabilizing Depth First Search (DFS) spanning tree algorithm, whose output is a DFS spanning tree of the communication graph, kept in a distributed fashion. keywords: distributed computing, fault tolerance. Department of Computer Science, The Technion, Haifa 32000, Israel. y Department of Computer Science, Texas A&M University, College Station, TX 77843, Contact Author: shlomi@cs.tamu.edu. Supported in part by TAMU Engineering Excellence funds and NSF Presidential Young Investigator Award CCR-91-58478. 1 Introduction A distributed algorithm is self-stabilizing, if it can be started from any possible global state and once started, the algorithm regains consistency by itself. The self-stabilization property is very useful for systems in which processors may crash and the...

A new paradigm for the design of self-stabilizing distributed algorithms, called local detection, is introduced. The essence of the paradigm is in defining a local condition based on the state of a processor and its immediate neighborhood, such that the system is in a globally legal state if and only if the local condition is satisfied at all the nodes. In this work we also extend the model of self-stabilizing networks traditionally assuming memory failure to include the model of dynamic networks (assuming edge failures and recoveries). We apply the paradigm to the extended model which we call "dynamic self-stabilizing networks. " Without loss of generality, we present the results in the least restrictive shared memory model of read/write atomicity, to which end we construct basic information transfer primitives. Using local detection, we develop deterministic and randomized self-stabilizing algorithms that maintain a rooted spanning tree in a general network whose topology changes dynamically. The deterministic algorithm assumes unique identities while the randomized assumes an anonymous network. The algorithms use a constant number of memory words per edge in each node; and both The size of memory words and of messages is the number of bits necessary to represent a node identity (typically O(log n) bits where n is the size of the network). These algorithms provide for the easy construction of self-stabilizing protocols for numerous tasks: reset, routing, topology-update and self-stabilization transformers that automatically self-stabilize existing protocols for which local detection conditions can be defined.

svasu,kurose,towsley¡

The well-known problem of leader election in distributed systems is considered in a dynamic context where processes may participate and crash spontaneously. Processes communicate by means of buffered broadcasting as opposed to usual point-to-point communication. In this paper we design a leader election protocol in such a dynamic system. As the problem at hand is considerably complex we adopt a step-wise refinement design method starting from a simple leader election protocol. In a first refinement a symmetric solution is obtained and eventually a fault-tolerant protocol is constructed. This gives rise to three protocols. The worst case message complexity of all protocols is analyzed. A formal approach to the verification of the leader election protocols is adopted. The requirements are specified in a property-oriented way and the protocols are denoted by means of extended finite state machines. It is proven using linear-time temporal logic that the protocols satisfy their requirements...

Abstract. This paper considers the self-stabilizing leader-election problem in a model of interacting anonymous finite-state agents. Leader election is a fundamental problem in distributed systems; many distributed problems are easily solved with the help of a central coordinator. Selfstabilizing algorithms do not require initialization in order to operate correctly and can recover from transient faults that obliterate all state information in the system. Anonymous finite-state agents model systems of identical simple computational nodes such as sensor networks and biological computers. Self-stabilizing leader election is easily shown to be impossible in such systems without additional structure. An eventual leader detector Ω? is an oracle that eventually detects the presence or absence of a leader. With the help of Ω?, uniform selfstabilizing leader election algorithms are presented for two natural classes of network graphs: complete graphs and rings. The first algorithm works under either a local or global fairness condition, whereas the second requires global fairness. With only local fairness, uniform self-stabilizing leader election in rings is impossible, even with the help of Ω?.

We relax the assumption of a synchronous distributedsystem in our Asynchronous Extrema Finding Algorithm (AEFA) and also allow the topology to change during theelection process. In AEFA, nodes can start the process of election at different times, but eventually after topologicalchanges stop long enough for the algorithm to terminate, all nodes agree on a unique leader. Our algorithm has beenproven to be "weakly " self-stabilizing.