A termination detection protocol and its formal verification

doi:10.1016/0743-7315(88)90033-0

Journal of Parallel and Distributed Computing

Volume 5, Issue 1, February 1988, Pages 82-91

https://doi.org/10.1016/0743-7315(88)90033-0 Get rights and content

Abstract

The purpose of this paper is twofold: First, we present a new and very simple protocol, which solves the termination detection protocol in any undirected communication network. The solution is based on symmetric knowledge: all processors are programmed equally, and an upper bound of the size of the network is the only global knowledge the processors need to know. Second, we formally prove the correctness of the protocol. The nature of the protocol allows us to describe all computations of the protocol as a language. This formalism introduces a new way of proving the correctness of the distributed algorithm.

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Cited by (7)

Distributed termination detection for dynamic systems
1997, Parallel Computing
A symmetric algorithm for detecting the termination of a distributed computation is presented. The algorithm does not require global information concerning the system and does not assume any communication features, barring finite delays in the delivery of messages. It permits dynamic creation and destruction of processes participating in the computation, and also permits destruction of a process by external processes, such as the OS kernel. It also provides for external processes spontaneously joining an ongoing computation. Proofs of safety and liveness are provided.
A distributed-termination experiment on a mesh-connected array of processors
1992, Parallel Computing
In totally asynchronous computation any number of processing elements (PEs) may start simultaneously. Termination detection for it is difficult because of asynchronousness and lack of single root (initiator) to accumulate termination information. This paper presents a symmetric, asynchronous, and distributed solution to the above problem for a mesh-connected array of PEs and its implementation and comparison on a parallel computer. Our algorithm produces less messages for termination purpose than the various counter token schemes. The worst time for it to finish is O(√n), where n is the number of PEs on a square mesh. An experiment on a 64-node NCUBE, parallel computer showed that it was at least twice as fast as a centralized termination detection algorithm.
The algorithm makes three assumptions: only nearest-neighbor communication exists; activation messages are always broadcast to all neighboring PEs to avoid deadlock; and any number of PEs can initiate the computation. It defines tokens and dependency arcs: tokens to collect termination states of regions of the mesh and dependency arcs to establish terminating precedence among connected PEs. They together reduce the number of messages for termination detection. Two sufficient conditions are shown to guarantee that any one of the PEs may detect termination.
Although the algorithm was originated for use with totally asynchronous computations for the finite element analysis, it is applicable to any iterative computations on a mesh.
Termination detection by using distributed snapshots
1989, Information Processing Letters
Distributing unit size workload packages in heterogeneous networks
2006, Journal of Graph Algorithms and Applications
On the memory overhead of distributed snapshots
1999, Networks
Development of a Class of Distributed Termination Detection Algorithms
1992, IEEE Transactions on Knowledge and Data Engineering

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Regular articleA termination detection protocol and its formal verification

Abstract

Inform. Process. Lett.

Distributed snapshots: Determining global states of distributed systems

ACM Trans. Comput. Systems

Regular article
A termination detection protocol and its formal verification