The chanciness of time

TL;DR

This paper introduces a new way to model digital network concurrency using history graphs, replacing global snapshots with local snapshots to better represent simultaneous events and network dynamics.

Contribution

It reformulates token games with local snapshots, enabling accurate representation of concurrent events and network changes without relying on global snapshots.

Findings

History graphs effectively model concurrent network events.

Local snapshots capture actions without central clock dependency.

The approach handles unpredictable network changes.

Abstract

Digital network failures stemming from instabilities in measurements of temporal order motivate attention to concurrent events. A century of attempts to resolve the instabilities have never eliminated them. Do concurrent events occur at indeterminate times, or are they better seen as events to which the very concept of temporal order cannot apply? Logical dependencies of messages propagating through digital networks can be represented by marked graphs on which tokens are moved in formal token games. However, available mathematical formulations of these token games invoke "markings" -- global snapshots of the locations of tokens on the graph. The formulation in terms of global snapshots is misleading, because distributed networks are never still: they exhibit concurrent events inexpressible by global snapshots. We reformulate token games used to represent digital networks so as to express concurrency. The trick is to replace global snapshots with "local snapshots." Detached from any central clock, a local snapshot records an action at a node during a play of a token game. Assemblages of local records define acyclic directed graphs that we call history graphs. We show how history graphs represent plays of token games with concurrent motions, and, importantly, how history graphs can represent the history of a network operating while undergoing unpredictable changes.