一句话：把 Milner 的进程表达式重新解释为完备度量空间上的收缩算子，从而给出分形等价的可判定公理化。
论文在迭代函数系统（IFS）所生成分形集的理论与进程演算之间建立联系。作者将 Milner 用于描述进程的表达式重新解释为完备度量空间上的收缩算子：当该空间取平面等具体空间时，不动点项的指称恰好对应熟悉的自相似分形集。基于此，作者研究“分形等价”——即在所有解释下都构造出相同自相似集合的项对所构成的同余关系——并给出其可靠且完备的公理化，证明过程中借用了进程演算的重要结果，例如 Rabinovich 关于迹等价的完备性定理。文章还进一步把结果与带标号 Markov 链以及不变测度联系起来，并在给出主要结论之外提出了一系列关于分形与进程演算的开放问题。
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric space. When the space is, for example, the plane, the denotations of fixed point terms correspond to familiar fractal sets. We give a sound and complete axiomatization of fractal equivalence, the congruence on terms consisting of pairs that construct identical self-similar sets in all interpretations. We further make connections to labelled Markov chains and to invariant measures. In all of this work, we use important results from process calculi. For example, we use Rabinovich's completeness theorem for trace equivalence in our own completeness theorem. In addition to our results, we also raise many questions related to both fractals and process calculi.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{SchmidNM23,
title = {Fractals from Regular Behaviours},
author = {Todd Schmid and Victoria Noquez and Lawrence S. Moss},
journal = {Logical Methods in Computer Science},
volume = {Volume 21, Issue 2},
year = {2025},
doi = {10.46298/lmcs-21(2:25)2025}
}