A Categorical Semantics for Bounded Petri Nets
arXiv:2101.09100 · doi:10.4204/EPTCS.372.5
Abstract
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.
arXiv commentIn Proceedings ACT 2021, arXiv:2211.01102
References in corpus (10)
- The Classification of Two-Dimensional Extended Topological Field Theories
- A Compositional Framework for Reaction Networks
- Open Petri Nets
- Connector algebras for C/E and P/T nets' interactions
- Executions in (Semi-)Integer Petri Nets are Compact Closed Categories
- Computational Petri Nets: Adjunctions Considered Harmful
- The Mathematical Specification of the Statebox Language
- A Small Universal Petri Net
- Nets with Mana: A Framework for Chemical Reaction Modelling
- Categories of Nets