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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:…

Category Theory · Mathematics 2025-07-30 Benjamin Merlin Bumpus , Sophie Libkind , Jordy Lopez Garcia , Layla Sorkatti , Samuel Tenka

The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based…

Data Analysis, Statistics and Probability · Physics 2012-05-21 Jukka-Pekka Onnela , Daniel J. Fenn , Stephen Reid , Mason A. Porter , Peter J. Mucha , Mark D. Fricker , Nick S. Jones

Reversible computation is an emerging computing paradigm that allows any sequence of operations to be executed in reverse order at any point during computation. Its appeal lies in its potential for lowpower computation and its relevance to…

Logic in Computer Science · Computer Science 2023-11-02 Kamila Barylska , Anna Gogolinska , Lukasz Mikulski , Anna Philippou , Marcin Piatkowski , Kyriaki Psara

Many monoidal-type objects are known to be classified by maps from the Catalan simplicial set $\mathbb{C}$ to various nerves of categories and higher categories. There are, for example, three different nerves of the 2-category of categories…

Category Theory · Mathematics 2015-07-21 Aaron Greenspan

In Petri net synthesis we ask whether a given transition system $A$ can be implemented by a Petri net $N$. Depending on the level of accuracy, there are three ways how $N$ can implement $A$: an embedding, the least accurate implementation,…

Formal Languages and Automata Theory · Computer Science 2023-06-22 Raymond Devillers , Ronny Tredup

In this paper, domination in Signed Petri net(SPN) has been introduced.We identify some of the Petri net structures where a dominating set can exist.Applications of producer consumer problem, searching of food by bees and finding similarity…

Discrete Mathematics · Computer Science 2020-01-14 Payal , Sangita Kansal

It is well-known that combinatorial circuits are modeled mathematically by string diagrams in a monoidal category. Given a gate set $\Sigma$, the circuits over $\Sigma$ can be thought of as string diagrams in the free monoidal category…

Quantum Physics · Physics 2025-01-23 Scott Wesley

The recently introduced notions of guarded traced (monoidal) category and guarded (pre-)iterative monad aim at unifying different instances of partial iteration whilst keeping in touch with the established theory of total iteration and…

Programming Languages · Computer Science 2019-02-07 Sergey Goncharov , Julian Jakob , Renato Neves

For a large Markovian model, a "product form" is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here…

Discrete Mathematics · Computer Science 2012-04-17 Serge Haddad , Jean Mairesse , Hoang-Thach Nguyen

Long before the invention of Feynman diagrams, engineers were using similar diagrams to reason about electrical circuits and more general networks containing mechanical, hydraulic, thermodynamic and chemical components. We can formalize…

Category Theory · Mathematics 2018-11-22 John C. Baez , Brandon Coya , Franciscus Rebro

This paper explores the problem of determining which classes of Petri nets can be encoded into behaviourally-equivalent CCS processes. Most of the existing related literature focuses on the inverse problem (i.e., encoding process calculi…

Programming Languages · Computer Science 2024-04-23 Benjamin Bogø , Andrea Burattin , Alceste Scalas

Computing steady-state distributions in infinite-state stochastic systems is in general a very dificult task. Product-form Petri nets are those Petri nets for which the steady-state distribution can be described as a natural product…

Performance · Computer Science 2017-08-22 Patricia Bouyer , Serge Haddad , Vincent Jugé

In this thesis, we present a flexible framework for specifying and constructing operads which are suited to reasoning about network construction. The data used to present these operads is called a \emph{network model}, a monoidal variant of…

Category Theory · Mathematics 2021-01-20 Joe Moeller

Initial semantics aims to capture inductive structures and their properties as initial objects in suitable categories. We focus on the initial semantics aiming to model the syntax and substitution structure of programming languages with…

Programming Languages · Computer Science 2025-02-18 Thomas Lamiaux , Benedikt Ahrens

New subclasses of Petri nets - Petri nets receptors and Petri nets effectors are introduced. The introduction/exclusion of such substructures in the main Petri net may be fulfilled in accordance with the Fusion/Defusion principles. We…

Logic in Computer Science · Computer Science 2020-01-14 Alexander Yu. Chunikhin , Marina D. Sviatnenko

Context: Petri net slicing is a technique to reduce the size of a Petri net to ease the analysis or understanding of the original Petri net. Objective: Presenting two new Petri net slicing algorithms to isolate those places and transitions…

Programming Languages · Computer Science 2024-02-14 Marisa Llorens , Javier Oliver , Josep Silva , Salvador Tamarit

During the last decade, various approaches have been put forward to integrate business processes with different types of data. Each of such approaches reflects specific demands in the whole process-data integration spectrum. One particular…

Artificial Intelligence · Computer Science 2020-06-12 Silvio Ghilardi , Alessandro Gianola , Marco Montali , Andrey Rivkin

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of one-counter automata with only a weak test for zero. We show that weak simulation preorder is decidable for OCN and that weak…

Formal Languages and Automata Theory · Computer Science 2014-06-17 Piotr Hofman , Richard Mayr , Patrick Totzke

Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in Petri net models can represent the control flow state or resources produced/consumed by transition firings. We define a resource as a part (a…

Logic in Computer Science · Computer Science 2023-06-22 Irina Lomazova , Vladimir Bashkin , Petr Jančar

Petri nets and their variants are often considered through their interleaved semantics, i.e. considering executions where, at each step, a single transition fires. This is clearly a miss, as Petri nets are a true concurrency model. This…

Logic in Computer Science · Computer Science 2025-02-05 Amazigh Amrane , Hugo Bazille , Uli Fahrenberg , Loïc Hélouët , Philipp Schlehuber-Caissier