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

Self-Stabilizing Universal Algorithms

. We prove the existence of a "universal" self-stabilizing algorithm, i.e., an algorithm which allows to stabilize a distributed system to a desired behaviour (as long as an algorithm stabilizing to that behaviour exists). Previous proposals required drastic increases in asymmetry and knowledge in order to work, while our algorithm does not use any additional knowledge, and does not require more symmetry-breaking conditions than available; thus, it is also stabilizing with respect to changes in the topology and in the identifiers assigned to each processor. We prove a tight quiescence time n + # for a synchronous network of n processors and diameter #. The algorithm can be made finite state with a negligible multiplicative loss. If the activation is asynchronous, we propose an algorithm with O(#n 2 ) quiescence time. Our results are true for a wide variety of sharedmemory models, including unidirectional, wireless and uniform networks. 1 Introduction A system is self-stabilizing i..