The lattice agreement problem in distributed systems

The lattice agreement problem is an important decision problem in distributed systems. It has applications in implementing atomic snapshot objects and building a special class of replicated state machines. In this work, we design novel algorithms for the lattice agreement problem in a variety of settings. We first focus on distributed message passing systems with only crash failures. Then we switch our attention to message passing systems with Byzantine failures. At last, we explore the application of lattice agreement in implementing linearizable and sequentially consistent snapshot objects.