The Heartbeat Failure Detector of the present invention, is a new, simple method and device that has several identical modules, and each module is attached to a processor in the system. Roughly speaking, the module of a processor x maintains a heartbeat counter for every other process. For each process y, the counter of y at x (called the heartbeat of y at x) periodically increases while y is alive and in the same network partition, and the counter stops increasing after y crashes or becomes partitioned away. Using such a device, x can solve the communication problem above by resending m only if the heartbeat of y at x increases. Note that if y is crashed (or partitioned away from x), its heartbeat at x stops almost immediately, and so x will also immediately stop sending copies of m to y.