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This paper studies the lattice agreement problem in asynchronous systems andexplores its application to building linearizable replicated state machines(RSM). First, we propose an algorithm to solve the lattice agreement problem in$O(\log f)$ asynchronous rounds, where $f$ is the number of crash failures thatthe system can tolerate. This is an exponential improvement over the previousbest upper bound. Second, Faleiro et al have shown in [Faleiro et al. PODC,2012] that combination of conflict-free data types and lattice agreementprotocols can be applied to implement linearizable RSM. They give a Paxos stylelattice agreement protocol, which can be adapted to implement linearizable RSMand guarantee that a command can be learned in at most $O(n)$ message delays,where $n$ is the number of proposers. Later on, Xiong et al in [Xiong et al.DISC, 2018] give a lattice agreement protocol which improves the $O(n)$guarantee to be $O(f)$. However, neither protocols is practical for building alinearizable RSM. Thus, in the second part of the paper, we first give animproved protocol based on the one proposed by Xiong et al. Then, we implementa simple linearizable RSM using the our improved protocol and compare ourimplementation with an open source Java implementation of Paxos. Results showthat better performance can be obtained by using lattice agreement basedprotocols to implement a linearizable RSM compared to traditional consensusbased protocols.

Linearizable Replicated State Machines with Lattice Agreement