arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2108.07510cs.LOcs.DCcs.MA
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可重构广播网络和异步共享内存系统是等价的(长版本)

Reconfigurable Broadcast Networks and Asynchronous Shared-Memory Systems are Equivalent (Long Version)

A. R. Balasubramanian, Chana Weil-Kennedy

摘要:

我们证明了两个分布式计算模型,即可重构广播网络(RBN)和异步共享内存系统(ASMS),这是独立介绍的等价性。RBN和ASMS都是一组匿名、有限状态进程运行相同协议的系统。在RBN中,进程通过选择性广播进行通信:一个进程可以广播一条消息,该消息被它的所有邻居接收,并且进程的邻居集合可以随时间任意改变。在ASMS中,进程通过共享内存进行通信:进程可以对共享寄存器进行写操作或读操作。我们的主要结果是,RBN和ASMS可以相互模拟,即它们在参数化可达性方面是等价的,其中我们给出两组(可能是无限的)配置C和C',它们由每个状态中进程数量的上下界定义,我们想决定C中的某些配置是否可以达到C'中的某些配置。使用这种模拟等价性,我们将RBN的结果转移到ASMS,反之亦然。最后,我们证明了RBN和ASMS可以模拟第三种分布式模型,称为即时观察(IO)网。此外,对于一个稍微强一些的模拟概念(本文给出的所有模拟都满足这个概念),我们证明了IO网不能模拟RBN。

英文摘要:

We show the equivalence of two distributed computing models, namely reconfigurable broadcast networks (RBN) and asynchronous shared-memory systems (ASMS), that were introduced independently. Both RBN and ASMS are systems in which a collection of anonymous, finite-state processes run the same protocol. In RBN, the processes communicate by selective broadcast: a process can broadcast a message which is received by all of its neighbors, and the set of neighbors of a process can change arbitrarily over time. In ASMS, the processes communicate by shared memory: a process can either write to or read from a shared register. Our main result is that RBN and ASMS can simulate each other, i.e. they are equivalent with respect to parameterized reachability, where we are given two (possibly infinite) sets of configurations C and C' defined by upper and lower bounds on the number of processes in each state and we would like to decide if some configuration in C can reach some configuration in C'. Using this simulation equivalence, we transfer results of RBN to ASMS and vice versa. Finally, we show that RBN and ASMS can simulate a third distributed model called immediate observation (IO) nets. Moreover, for a slightly stronger notion of simulation (which is satisfied by all the simulations given in this paper), we show that IO nets cannot simulate RBN.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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