A Categorical Semantics for Bounded Petri Nets

A Categorical Semantics for Bounded Petri Nets

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 f...

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Veröffentlicht in:arXiv.org 2022-11
Hauptverfasser: Fabrizio Romano Genovese, Loregian, Fosco, Palombi, Daniele
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Computer Science - Formal Languages and Automata Theory
Computer Science - Logic in Computer Science
Mathematics - Category Theory
Petri nets
Semantics
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Loregian, Fosco
Palombi, Daniele
description 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.
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subjects Computer Science - Formal Languages and Automata Theory
Computer Science - Logic in Computer Science
Mathematics - Category Theory
Petri nets
Semantics
title A Categorical Semantics for Bounded Petri Nets
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