Fine-Grain Multitolerant Barrier Synchronization

We design a multitolerant program for synchronizing the phases of concurrent processes. The tolerances of the program enable processes to (i) compute all phases correctly in the presence of faults that corrupt process state in a detectable manner, and (ii) compute only a minimum possible number of phases incorrectly before resuming correct computation in the presence of faults that corrupt process state in an undetectable manner. The program is ne-grain in the sense that each process action either updates the state of that process or involves communication with one of two neighboring processes. 1 Motivation Barrier synchronization in its general form requires that a set of processes execute a cyclic sequence of phases so that a phase is executed by each process only after all processes have completed the previous phase. This form of synchronization generalizes a variety of others, such as clock unison, phase synchronization and atomic commitment, and appears frequently in parallel, distributed, and scientiic computation applications. Often the design of barrier synchronization has to accommodate the occurrence of faults. Commonly considered examples of faults include incorrect initializations; corruption, loss, reordering, and duplication of messages; processor restarts; and performance and timing violations. While some of these fault-classes can be masked (i.e., even in their presence each phase is executed correctly), others cannot. To accommodate multiple fault-classes, not all of which can be masked, it is convenient to view the eeect of faults in each fault-class as a \corruption" of the state of some process, i.e., the state of that process prior to the fault is lost and is replaced with some other value. The state corruption view suggests that one way to accommodate all of the fault-classes is to design the set of processes to be stabilizing 2], i.e., to recover from an arbitrarily corrupted state to one from where the speciication of barrier synchronization is (re)satissed. Unfortunately, a stabilizing design allows incorrect execution of (a nite number of) phases in the presence of each fault-class before the recovery is complete, and it is thus not ideal for the fault-classes that can be masked. We therefore present in this paper barrier synchronization designs that ooer multiple levels of tolerance corresponding to multiple fault-classes, a notion which we refer to as multitolerance 3].