Marc Jalfon

Token management schemes and random walks yield self-stabilizing mutual exclusion

A self-stabilizing system is a system which reaches a legal configuration by itself, without any kind of an outside intervention; when started from any arbitrary configuration. Hence a self-stabilizing system accommodates any possible initial configuration and tolerates transient bugs. This fact contributes most of the extra difficulty of devising selfstabilizing systems. On the other hand, the same fact makes self-stabilizing systems so appealing as no initialization of the system is required. In this paper a novel modular method for constructing uniform self stabilizing mutual exclusion (or in short USSA4E) protocols is presented. The viability of the method is demonstrated by constructing for the first time a randomized USSME protocol for any arbitrary dynamic graph and another one for dyna.mic rings. The correctness of both protocols is proved and their complexity is analyzed. The analysis of the new protocols in*Partially supported by VPR Funds Japan TS Research Fund and B. Sr. G. Greenberg Research Fund (Ottawa). tpartially supported by a Gutwirth fellowship. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and /or specific permission.

Self-Stabilizing Ring Orientation

A self-stabilizing system is a distributed system which can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of an outside intervention. A ring is a distributed system in which all processors are connected in a ring. A ring is oriented if all processors in the ring agree on common right and left directions. A protocol is uniform if all processors use the same program.