On causal broadcasting with positive acknowledgments and bounded-length counters

A causal broadcast protocol was proposed earlier in [R. Baldoni (1998)]. Two extensions of the protocol were also proposed in order to improve its throughput and bandwidth utilization. We show that both extensions are not live, i.e., there may be execution patterns in which processes stop delivering messages. We also show that the algorithm for the second extension does not satisfy the requirements on which its correctness was established. Finally, we provide fixed versions of both extensions and prove their correctness.