Additive Invariants of Open Petri Nets
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915414948184064 |
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| author | Bumpus, Benjamin Merlin Libkind, Sophie Garcia, Jordy Lopez Sorkatti, Layla Tenka, Samuel |
| author_facet | Bumpus, Benjamin Merlin Libkind, Sophie Garcia, Jordy Lopez Sorkatti, Layla Tenka, Samuel |
| contents | We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems: one for open Petri nets and one for monically open Petri nets (i.e. open Petri nets whose interfaces are specified by monic maps). Our results can be summarized as follows. The additive invariants of open Petri nets are completely determined by their values on a particular class of single-transition Petri nets. However, for monically open Petri nets, the additive invariants are determined by their values on transitionless Petri nets and all single-transition Petri nets. Our results confirm a conjecture of John Baez (stated during the AMS' 2022 Mathematical Research Communities workshop). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01643 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Additive Invariants of Open Petri Nets Bumpus, Benjamin Merlin Libkind, Sophie Garcia, Jordy Lopez Sorkatti, Layla Tenka, Samuel Category Theory Molecular Networks We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems: one for open Petri nets and one for monically open Petri nets (i.e. open Petri nets whose interfaces are specified by monic maps). Our results can be summarized as follows. The additive invariants of open Petri nets are completely determined by their values on a particular class of single-transition Petri nets. However, for monically open Petri nets, the additive invariants are determined by their values on transitionless Petri nets and all single-transition Petri nets. Our results confirm a conjecture of John Baez (stated during the AMS' 2022 Mathematical Research Communities workshop). |
| title | Additive Invariants of Open Petri Nets |
| topic | Category Theory Molecular Networks |
| url | https://arxiv.org/abs/2303.01643 |