有界Petri网的范畴语义
A Categorical Semantics for Bounded Petri Nets
摘要：
我们提供了一个范畴语义有界Petri网，无论是在集体和个人令牌哲学。在这两种情况下，我们描述了一个网络内部绑定的过程，通过使用comonads构建新的网络执行类别，外部使用lax-monoidal-lax函子。我们的外部语义是非局部的，这意味着令牌被赋予了一些关于网络全局状态的属性。然后，我们证明，在这两种情况下，内部和外部的建设是等效的，通过使用机器建立在顶部的Grothendieck建设。单个令牌的情况更困难，因为它需要更明确地依赖抽象方法。
英文摘要：
We provide a categorical semantics for bounded Petri nets, both in the collective- and individual-token philosophy. In both cases, we describe the process of bounding a net internally, by just constructing new categories of executions of a net using comonads, and externally, using lax-monoidal-lax functors. Our external semantics is non-local, meaning that tokens are endowed with properties that say something about the global state of the net. We then prove, in both cases, that the internal and external constructions are equivalent, by using machinery built on top of the Grothendieck construction. The individual-token case is harder, as it requires a more explicit reliance on abstract methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
