Beyond Lamport’s Happened-Before: On the Role of Time Bounds in Synchronous Systems

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Abstract

Lamport’s Happened-before relation is fundamental to coordinating actions in asynchronous systems. Its role is less dominant in synchronous systems, in which bounds are available on transmission times over channels. This paper initiates a study of the role that time bounds play in synchronous systems by focusing on two classes of problems: Ordered Response, in which a triggering event must be followed by a sequence of events (“responses”) performed in a prescribed temporal order, and Simultaneous Response, in which the responses must be performed simultaneously. In both cases, information about the triggering event must flow from its site of origin to the responding sites, and the responses must be timed as specified. A generalization of happened- before called Syncausality, is defined. A pattern of communication consisting of a syncausal chain coupled with an appropriate set of time bound guarantees gives rise to a communication structure called a centipede. Centipedes are a nontrivial generalization of message chains, and their existence is shown to be necessary in every execution of every protocol that solves ordered response. A variation on centipedes called centibrooms are shown to play an analogous role for Simultaneous Response: Every execution of a protocol for Simultaneous Response must contain a centibroom.