Problem
Research questions and friction points this paper is trying to address.
causal graph rewriting
asynchronous computation
directed acyclic graphs
non-determinism
locality constraints
Causal graph rewriting
🤖 AI Summary
提出因果图重写模型，通过异步应用局部规则于有向无环图上解决计算非确定性问题，并研究了其局部性和序列组合性质。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
causal graph rewriting
asynchronous computation
directed acyclic graphs
locality preservation
cellular automaton simulation
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