Dialectica Petri Nets

TL;DR

This paper explores a generalized categorical framework for Petri nets using the Dialectica construction, enabling modeling of various transition types like truth-values, probabilities, and rates within a unified structure.

Contribution

It extends the Dialectica-based categorical model to encompass Petri nets with diverse transition types evaluated in different algebraic structures called lineales.

Findings

Unified categorical framework for diverse Petri net transitions

Modeling of truth-values, probabilities, and rates in the same category

Connections to recent models of categorical nets

Abstract

The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets generalising the original application to suggest that Petri nets with different kinds of transitions can be modelled in the same categorical framework. Transitions representing truth-values, probabilities, rates or multiplicities, evaluated in different algebraic structures called lineales are useful and are modelled here in the same category. We investigate (categorical instances of) this generalised model and its connections to more recent models of categorical nets.