10 Selected Papers Engineering ▲Reprinted from Information Sciences, 180, Yukiko Yamauchi et al., Timer-based composition of fault-containing self-stabilizing protocols, 1802-1816, Copyright(2010), with permission from Elsevier. Reprinted from Information Sciences, 180, Yukiko Yamauchi et al., Timer-based composition of fault-containing self-stabilizing Timer-based Composition of Fault-containing Self-stabilizing Protocols Paper in journals: this is the irst page of a paper published in Information Sciences. [Information Sciences] 180, 1802-1816(2010) The following is a comment on the published paper shown on the preceding page. Introduction Large scale distributed systems have been developed recently. As the number of processes in a distributed system grows, the distributed system becomes more prone to faults. Self- stabilization [1] provides autonomous adaptability to any inite number and any kind of transient faults (e.g., memory soft error at processes). Even when a distributed system is corrupted by transient faults and gets into an unexpected coniguration, a self- stabilizing system can autonomously recover its desired behav- ior without any external intervention. Although self-stabiliza- tion promises autonomous adaptability to any scale of transient faults, the adaptability to small scale faults is more important in practice. This is because catastrophic faults rarely occur in practical environments and small scale faults are more likely to occur. Nevertheless, self-stabilization promises nothing during the recovery and the effect of small scale faults can spread over the entire network. A self-stabilizing system can be contamin- ated entirely even by small scale faults while we expect that the system can recover quickly with small effect from small scale faults. A fault-containing self-stabilizing protocol [2] promises self- stabilization against large scale faults and fault-containment against small scale faults (Figure 1). Starting from any conig- uration corrupted by f processes or less, an f-fault-containing protocol reaches a legitimate configuration with small effect and in short time, i.e., both the recovery time and the number of processes affected by the faults are proportional to f or less. So, the fault-containment property improves the adaptability of self- stabilization to small scale faults. Hierarchical composition of protocols facilitates the design of new protocols. In hierarchical composition of two (or more) protocols, the output of one protocol (called the lower protocol) is used as the input to the other (called the upper protocol), and the obtained protocol provides the output of the upper protocol for the input to the lower protocol. Hierarchical composition of protocols is commonly used to relieve the dificulty in designing self-stabilizing protocols. Dif- ferent from composition of classical (or non-self-stabilizing) protocols, protocol composition based on sequential execution of protocols is impossible for self-stabilizing protocols. Instead, the adaptability to any coniguration of self-stabilizing protocols allows us to composite protocols based on parallel execution of protocols. However, the composition technique cannot preserve the fault-containment property of the source protocols. This is because the parallel execution of the source protocols allows the upper protocol to execute its actions before stabilization of the lower protocol, that is, the upper protocol can work on an incorrect intermediate output of the lower protocol (Figure 2). Containment-preserving composition of self-stabilizing protocols In this paper, we propose, as a novel composition technique of fault-containing self-stabilizing protocols, a containment- preserving composition technique, RWFC-LNS (Recovery Waiting Fault-containing Composition with the Local Neighbor- hood Synchronizer). The composition technique follows a gen- eral strategy, RWFC strategy, which was previously proposed by the authors [3]. The RWFC strategy realizes containment- preserving composition of self-stabilizing protocols by forcing the upper protocol to stop its execution until the lower protocol completes the recovery from a faulty coniguration. This strat- egy guarantees that the upper protocol always works on the cor- rect input from the lower protocol. Therefore, the upper protocol can recover from a faulty coniguration with keeping its fault- containment property. The key to implementation of the RWCF strategy is how the waiting at the upper protocol is realized. In the RWFC-LNS technique, the waiting at the upper protocol is realized using a synchronized timer at each process. Since we consider asynchronous systems, we design self-stabilizing syn- Timer-based Composition of Fault-containing Self-stabilizing Protocols MASUZAWA Toshimitsu and KAKUGAWA Hirotsugu (Graduate School of Information Science and Technology) 25 ANNUAL REPORT OF OSAKA UNIVERSITY – Academic Achievements – 2010-2011 26 ANNUAL REPORT OF OSAKA UNIVERSITY – Academic Achievements – 2010-2011