Motivated by recent distributed systems technology, Aguilera et al. introduced a hybrid model of distributed computing, called the message-and-memory model or m&m model for short. In this model, processes can communicate by message passing and also by accessing some shared memory (e.g., through some RDMA connections). We first consider the basic problem of implementing an atomic single-writer multi-reader (SWMR) register shared by all the processes in m&m systems. Specifically, we give an algorithm that implements such a register in m&m systems and show that it is optimal in the number of process crashes that it tolerates. This generalizes the well-known ABD implementation of an atomic SWMR register in a pure message-passing system. We then combine our register implementation for m&m systems with a randomized consensus algorithm of Aspnes and Herlihy, and obtain a randomized consensus algorithm for m&m systems that is also optimal in the number of process crashes that it can tolerate. Finally, we determine the minimum number of RDMA connections that is sufficient to implement a SWMR register, or solve randomized consensus, in an m&m system with t process crashes, for any given t.

受最近分布式系统技术的启发，Aguilera 等人。引入了分布式计算的混合模型，称为消息和内存模型或简称m&m 模型。在这个模型中，进程可以通过消息传递和访问一些共享内存（例如，通过一些 RDMA 连接）进行通信。我们首先考虑实现所有共享的原子单写入器多读取器 (SWMR) 寄存器的基本问题m&m 系统中的过程。具体来说，我们给出了一种在 m&m 系统中实现这种寄存器的算法，并表明它在其容忍的进程崩溃次数方面是最佳的。这概括了纯消息传递系统中原子 SWMR 寄存器的众所周知的 ABD 实现。然后，我们将 m&m 系统的寄存器实现与 Aspnes 和 Herlihy 的随机共识算法相结合，并获得了 m&m 系统的随机共识算法，该算法在它可以容忍的进程崩溃次数方面也是最佳的。最后，对于任何给定的t，我们确定在具有t进程崩溃的 m&m 系统中足以实现 SWMR 寄存器或解决随机共识的最小 RDMA 连接数。