Graph Transformation Systems (GTS) and Petri Nets (PN) are two central, theoretically sound, formal models for concurrent or distributed systems. A lot of papers have focused on the relationship between GTS and PN. It is generally accepted that PN are instances of GTS due to the lack of ability to adapt or reconfigure their structure. In this paper, which extends a recent one, we reverse this perspective by presenting a formal definition of GTS in terms of Symmetric Nets (SN). SN are a standard High-Level PN formalism featuring a compact syntax which highlights behavioral symmetries of systems. The major strength lies in the possibility of using well-established tools to edit/efficiently analyze (SN-based) graph transformation models. We follow a structural approach, based on a newly implemented symbolic calculus, to validate Graph Transformation Rules (GTR) and formally verify GTS properties.

In the second part of the paper, we supply a semantic characterization of the SN-based graph transformation model, by carrying out a thorough comparison with the classical, algebraic double-pushout (DPO) approach. We constructively and formally show how to translate any DPO rule to a corresponding, elementary or composite, SN rule. We treat both injective and non-injective DPO rules/rule matches. The comparison shows that the SN approach is, in some sense, a generalization of the DPO.

图转换系统（GTS）和Petri网（PN）是并发或分布式系统的两个中心，理论上合理的形式化模型。许多论文都集中在GTS和PN之间的关系上。由于缺乏适应或重新配置其结构的能力，PN通常是GTS的实例。在本文的基础上，它扩展了最近的观点，我们通过用对称网络（SN）提出GTS的正式定义来扭转这种观点。SN是一种标准的高级PN形式主义，具有紧凑的语法，突出了系统的行为对称性。主要优势在于可以使用完善的工具来编辑/有效分析（基于SN的）图形转换模型。我们采用一种基于新实施的符号演算的结构化方法，

在本文的第二部分中，我们通过与经典的代数双推出（DPO）方法进行了彻底的比较，提供了基于SN的图转换模型的语义表征。我们以建设性和正式的方式展示了如何将任何DPO规则转换为相应的基本或复合SN规则。我们对待内射性和非内射性DPO规则/规则匹配。比较表明，从某种意义上说，SN方法是DPO的概括。