DeepAI AI Chat
Log In Sign Up

A Categorical Semantics for Bounded Petri Nets

by   Fabrizio Genovese, et al.

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.


page 1

page 2

page 3

page 4


A Categorical Semantics for Guarded Petri Nets

We build on the correspondence between Petri nets and frees ymmetric str...

Elements of Petri nets and processes

We present a formalism for Petri nets based on polynomial-style finite-s...

Token Multiplicity in Reversing Petri Nets Under the Individual Token Interpretation

Reversing Petri nets (RPNs) have recently been proposed as a net-basedap...

A Categorical Semantics for Hierarchical Petri Nets

We show how a particular flavor of hierarchical nets, where the firing o...

The ε-t-Net Problem

We study a natural generalization of the classical ϵ-net problem (Haussl...

Just Testing

The concept of must testing is naturally parametrised with a chosen comp...

Dialectica Petri nets

The categorical modeling of Petri nets has received much attention recen...