Related papers: Structural Liveness of Conservative Petri Nets
We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz and Reisig (processes are etale maps from graphs) and an…
We suggest to simulate evolution of complex organisms constrained by the sole requirement of robustness in their expression patterns. This scenario is illustrated by evolving discrete logical networks with epigenetic properties. Evidence…
We present an embedding of Petri nets into B abstract systems. The embedding is achieved by translating both the static structure (modelling aspect) and the evolution semantics of Petri nets. The static structure of a Petri-net is captured…
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…
A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. Characterizing the class of systems that are lucent is…
We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in…
In process mining, alignments quantify the degree of deviation between an observed event trace and a business process model and constitute the most important conformance checking technique. We study the algorithmic complexity of computing…
A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. This paper explores the class of marked Petri nets that…
Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex…
A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the Max-Flow Min-Cut Theorem to infinite networks and a short proof of a conjecture of Kropholler. This…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
The robustness of an ecological network quantifies the resilience of the ecosystem it represents to species loss. It corresponds to the proportion of species that are disconnected from the rest of the network when extinctions occur…
Process models are used by human analysts to model and analyse behaviour, and by machines to verify properties such as soundness, liveness or other reachability properties, and to compare their expressed behaviour with recorded behaviour…
We investigate in detail the model of a trophic web proposed by Amaral and Meyer [Phys. Rev. Lett. 82, 652 (1999)]. We focused on small-size systems that are relevant for real biological food webs and for which the fluctuations are playing…
We propose a method for checking generalized reachability properties in Petri nets that takes advantage of structural reductions and that can be used, transparently, as a pre-processing step of existing model-checkers. Our approach is based…
Place bisimilarity is a behavioral equivalence for finite Petri nets, proposed in \cite{ABS91} and proved decidable in \cite{Gor21}. In this paper we propose an extension to finite Petri nets with silent moves of the place bisimulation…
This study provides a foundational theoretical investigation into the mathematical existence and asymptotic properties of Ulanowicz's structural resilience. While ecological evidence suggests that sustainable systems gravitate toward an…
Synthesis for a type $\tau$ of Petri nets is the following search problem: For a transition system $A$, find a Petri net $N$ of type $\tau$ whose state graph is isomorphic to $A$, if there is one. To determine the computational complexity…
The stability of ecosystems as well as the relation between topology and dynamics on multilayer networks are important questions that are usually discussed in separate communities. Here, we combine these two topics by investigating the…
In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the…