因果图重写

中文摘要 AI 辅助

我们引入了因果图重写，这是一种计算模型，其中局部规则以异步方式应用于有向无环图。由异步性产生的非确定性受到有向边的约束，这些有向边必须被理解为计算依赖性和局部性约束——并且它们本身也受到重写的影响。我们通过两个例子来说明该模型：一个粒子系统，以及一个让人联想到广义相对论的时间膨胀例子。我们研究了诱导子图和图组合的良定义性及其性质，这些性质隔离并重新组合了受重写影响的区域。然后，我们研究了相对于这些构造的局部性，展示了局部重写如何保持位置、边界和上下文。我们的主要结果涉及顺序组合：局部性从单条规则的应用扩展到任意有效序列，因为任何局部规则自动是$*$-局部的和$*$-扩展的。我们还形式化并证明了对任意一维元胞自动机的模拟。

英文摘要

We introduce causal graph rewriting, a model of computation in which local rules are applied on directed acyclic graphs in an asynchronous manner. The non-determinism arising from asynchrony is disciplined by the oriented edges, which must be understood as both computational dependencies and locality constraints---and are themselves subject to the rewriting. We illustrate the model through two examples: a particle system, and a time-dilation example---reminiscent of general relativity. We study the well-definedness and properties of induced subgraphs and graph composition, which isolate and recombine the region affected by a rewrite. We then study locality with respect to these constructions, showing how a local rewrite preserves positions, borders, and context. Our main result concerns sequential composition: locality extends from single rule applications to arbitrary valid sequences, as any local rule is automatically $*$-local and $*$-extensive. We also formalise and prove the simulation of any one-dimensional cellular automaton.

发表机构

• Université Paris-Saclay（巴黎萨克雷大学）
• Inria（法国国家数字与数据科学研究所）
• CNRS（法国国家科学研究中心）
• Univ Paris Est Creteil（巴黎东 Créteil 大学）

机构由 AI 辅助整理，请以论文原文为准。