{"title":"Presheaf automata","authors":"Georg Struth, Krzysztof Ziemiański","doi":"arxiv-2409.04612","DOIUrl":null,"url":null,"abstract":"We introduce presheaf automata as a generalisation of different variants of\nhigher-dimensional automata and other automata-like formalisms, including Petri\nnets and vector addition systems. We develop the foundations of a language\ntheory for them based on notions of paths and track objects. We also define\nopen maps for presheaf automata, extending the standard notions of simulation\nand bisimulation for transition systems. Apart from these conceptual\ncontributions, we show that certain finite-type presheaf automata subsume all\nPetri nets, generalising a previous result by van Glabbeek, which applies to\nhigher-dimensional automata and safe Petri nets.","PeriodicalId":501135,"journal":{"name":"arXiv - MATH - Category Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Category Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04612","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce presheaf automata as a generalisation of different variants of
higher-dimensional automata and other automata-like formalisms, including Petri
nets and vector addition systems. We develop the foundations of a language
theory for them based on notions of paths and track objects. We also define
open maps for presheaf automata, extending the standard notions of simulation
and bisimulation for transition systems. Apart from these conceptual
contributions, we show that certain finite-type presheaf automata subsume all
Petri nets, generalising a previous result by van Glabbeek, which applies to
higher-dimensional automata and safe Petri nets.
我们介绍的预设自动机是对高维自动机和其他类似自动机形式的不同变体（包括 Petrinets 和向量加法系统）的概括。我们以路径和轨迹对象的概念为基础，为它们建立了语言理论的基础。我们还定义了预叶自动机的开放映射，扩展了过渡系统的标准模拟和双模拟概念。除了这些概念上的贡献之外，我们还证明了某些有限型预设自动机包含所有 Petri 网，从而推广了 van Glabbeek 以前的一个结果，该结果适用于高维自动机和安全 Petri 网。
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