Petri nets are monoids: a new algebraic foundation for net theory

[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science Pub Date : 1988-07-05 DOI:10.1109/LICS.1988.5114

J. Meseguer, U. Montanari

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引用次数: 92

Abstract

The composition and extraction mechanisms of Petri nets are at present inadequate. This problem is solved by viewing place/transition Petri nets as ordinary, directed graphs equipped with two algebraic operations corresponding to parallel and sequential composition of transitions. A distributive law between the two operations captures a basic fact about concurrency. Novel morphisms are defined, mapping single, atomic transitions into whole computations, thus relating system descriptions at different levels of abstraction. Categories equipped with products and coproducts (corresponding to parallel and nondeterministic compositions) are introduced for Petri nets with and without initial markings. It is briefly indicated how the approach yields function spaces and novel interpretations of duality and invariants. The results provide a formal basis for expressing the semantics of concurrent languages in terms of Petri nets and an understanding of concurrency in terms of algebraic structures over graphs and categories that should apply to other models and contribute to the conceptual unification of concurrency.<>

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Petri网是一元群:网络理论的一个新的代数基础

目前对Petri网的组成和提取机理的研究还不充分。通过将位置/转换Petri网视为普通的有向图来解决这个问题，这些图配备了对应于并行和顺序转换组合的两种代数操作。两个操作之间的分配律抓住了一个关于并发性的基本事实。定义了新的态射，将单个原子转换映射到整个计算中，从而将不同抽象级别的系统描述联系起来。为有和没有初始标记的Petri网引入了带有乘积和副乘积的类别(对应于平行和不确定性组合)。简要说明了该方法如何产生函数空间以及对偶性和不变量的新解释。这些结果为用Petri网来表达并发语言的语义提供了形式化的基础，并为用图和类别上的代数结构来理解并发提供了依据，这应该适用于其他模型，并有助于并发的概念统一。

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[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science

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