Linearizable Replicated State Machines With Lattice Agreement

This paper studies the lattice agreement problem in asynchronous systems and explores its application to building a linearizable replicated state machine (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 that the system can tolerate. This is an exponential improvement over the previous best upper bound of O(f). Second, Faleiro et al have shown in [Faleiro et al. PODC, 2012] that combination of conflict-free data types and lattice agreement protocols can be applied to implement a linearizable RSM. They give a Paxos style lattice agreement protocol, which can be adapted to implement a linearizable RSM and guarantee that a command by a client can be learned in at most O(n) message delays, where n is the number of proposers. Later, Xiong et al in [Xiong et al. DISC, 2018] gave a lattice agreement protocol which improves the O(n) message delay guarantee to O(f). However, neither of the protocols is practical for building a linearizable RSM. Thus, in the second part of the paper, we first give an improved protocol based on the one proposed by Xiong et al. Then, we implement a simple linearizable RSM using our improved protocol and compare our implementation with an open source Java implementation of Paxos. Results show that better performance can be obtained by using lattice agreement based protocols to implement a linearizable RSM compared to traditional consensus based protocols

Byzantine Lattice Agreement in Asynchronous Systems

We study the Byzantine lattice agreement (BLA) problem in asynchronous distributed message passing systems. In the BLA problem, each process proposes a value from a join semi-lattice and needs to output a value also in the lattice such that all output values of correct processes lie on a chain despite the presence of Byzantine processes. We present an algorithm for this problem with round complexity of O(log f) which tolerates f < n/5 Byzantine failures in the asynchronous setting without digital signatures, where n is the number of processes. This is the first algorithm which has logarithmic round complexity for this problem in asynchronous setting. Before our work, Di Luna et al give an algorithm for this problem which takes O(f) rounds and tolerates f < n/3 Byzantine failures. We also show how this algorithm can be modified to work in the authenticated setting (i.e., with digital signatures) to tolerate f < n/3 Byzantine failures

Lattice Agreement in Message Passing Systems

This paper studies the lattice agreement problem and the generalized lattice agreement problem in distributed message passing systems. In the lattice agreement problem, given input values from a lattice, processes have to non-trivially decide output values that lie on a chain. We consider the lattice agreement problem in both synchronous and asynchronous systems. For synchronous lattice agreement, we present two algorithms which run in log(f) and min{O(log^2 h(L)), O(log^2 f)} rounds, respectively, where h(L) denotes the height of the input sublattice L, f < n is the number of crash failures the system can tolerate, and n is the number of processes in the system. These algorithms have significant better round complexity than previously known algorithms. The algorithm by Attiya et al. [Attiya et al. DISC, 1995] takes log(n) synchronous rounds, and the algorithm by Mavronicolasa [Mavronicolasa, 2018] takes min{O(h(L)), O(sqrt(f))} rounds. For asynchronous lattice agreement, we propose an algorithm which has time complexity of 2*min{h(L), f + 1} message delays which improves on the previously known time complexity of O(n) message delays. The generalized lattice agreement problem defined by Faleiro et al in [Faleiro et al. PODC, 2012] is a generalization of the lattice agreement problem where it is applied for the replicated state machine. We propose an algorithm which guarantees liveness when a majority of the processes are correct in asynchronous systems. Our algorithm requires min{O(h(L)), O(f)} units of time in the worst case which is better than O(n) units of time required by the algorithm in [Faleiro et al. PODC, 2012]

Approaches to Conflict-free Replicated Data Types

Conflict-free Replicated Data Types (CRDTs) allow optimistic replication in a principled way. Different replicas can proceed independently, being available even under network partitions, and always converging deterministically: replicas that have received the same updates will have equivalent state, even if received in different orders. After a historical tour of the evolution from sequential data types to CRDTs, we present in detail the two main approaches to CRDTs, operation-based and state-based, including two important variations, the pure operation-based and the delta-state based. Intended as a tutorial for prospective CRDT researchers and designers, it provides solid coverage of the essential concepts, clarifying some misconceptions which frequently occur, but also presents some novel insights gained from considerable experience in designing both specific CRDTs and approaches to CRDTs.Comment: 36 page

Notes on Theory of Distributed Systems

Notes for the Yale course CPSC 465/565 Theory of Distributed Systems