基本对象系统中类覆盖问题的复杂性：数据网的解决方案

中文摘要 AI 辅助

基本对象系统（EOSs）是网中网（NWNs）范式中的一种模型，其中令牌可承载标准Petri网。我们研究EOSs上包括终止性和有界性在内的类覆盖问题的复杂性。由于EOSs上的覆盖性和有界性一般是不可判定的，我们聚焦于保守EOSs（cEOSs）这一相关片段。我们的技术将cEOSs解释到数据网框架中，数据网的令牌携带来自无限域的数据，从而连接了嵌套范式与数据感知范式。具体而言，我们证明cEOS的类覆盖问题等价于数据网中名为通道-νPNs（c-νPNs）的有趣片段上的类覆盖问题，该片段在νPN（具有全局新名称创建特性）的基础上扩展了带重命名的受限传输形式。c-νPNs的表达能力仍弱于无序数据网，后者具有有损名称创建以及强大的全位置操作和广播形式。这些归约使我们能够利用数据网的已知结果分析cEOS覆盖性，我们得出结论：cEOS覆盖性的复杂性是双阿克曼型的，为$\boldsymbol{\text{F}}_{\boldsymbol{\text{ω2}}}$完全问题，而终止性和有界性则是非原始递归的。

英文摘要

Elementary Object Systems (EOSs) are a model in the nets-within-nets (NWNs) paradigm, where tokens in turn can host standard Petri nets. We study the complexity of coverability-like problems, including termination and boundedness, over EOSs. Since coverability and boundedness are undecidable in general on EOSs, we focus on the relevant fragment of conservative EOSs (cEOSs). Our technique interprets cEOSs into the framework of data nets, whose tokens carry data from an infinite domain, thus bridging the nesting and the data-aware paradigms. Specifically, we show that cEOS coverability-like problems are equivalent to the coverability-like problems over an interesting fragment, called channel-$ν$PNs (c-$ν$PNs), of data nets that extends $ν$PN (featuring globally fresh name creation) with restricted forms of transfers with renaming. c-$ν$PNs remain less expressive than Unordered Data Nets, which feature lossy name creation as well as powerful forms of whole-place operations and broadcasts. These reductions allow us to analyze cEOS coverability taking advantage of known results on data nets. We conclude that the complexity of cEOS coverability is double-Ackermanian, $\mathcal{F}_{ω2}$-complete, while termination and boundedness are non-primitive recursive.

发表机构

• Free University of Bozen-Bolzano（博尔扎诺自由大学）
• Chennai Mathematical Institute（金奈数学研究所）
• IIT Dharwad（达瓦德印度理工学院）

机构由 AI 辅助整理，请以论文原文为准。