Related papers: Homogeneous Equations of Algebraic Petri Nets
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…
In this paper we investigate a relaxed concept of controllability, known in the literature as herdability, namely the capability of a system to be driven towards the(interior of the) positive orthant. Specifically, we investigate…
We construct moduli spaces of linear self-maps of projective space with marked points, up to projective equivalence. That is, we let the special linear group act simultaneously by conjugation on projective linear maps and diagonally on…
Petri Nets (PN) are a central, theoretically sound model for concurrent or distributed systems but, at least in their classical definition, not expressive enough to represent dynamic reconfiguration capabilities. On the other side,…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
This document demonstrates that the efficient approach for diagnosis of Petri nets via integer linear programming may be unable to detect a fault even if the system is diagnosable.
The increasing demand for automation and flexibility drives the widespread adoption of heterogeneous automated guided vehicles (AGVs). This work intends to investigate a new scheduling problem in a material transportation system consisting…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…
We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…
This paper analyses the stability of cycles within a heteroclinic network lying in a three-dimensional manifold formed by six cycles, for a one-parameter model developed in the context of game theory. We show the asymptotic stability of the…
Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…
P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…
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 power graph of a group $G$, denoted as $P(G)$, constitutes a simple undirected graph characterized by its vertex set $G$. Specifically, vertices $a,b$ exhibit adjacency exclusively if $a$ belongs to the cyclic subgroup generated by $b$…
Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We give a linear-algebraic approach to…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
Let $X$ be a non-singular irreducible complex projective curve of genus $g\geq 2$. We use $(t,\ell)$-stability to prove the existence of coherent systems over $X$ that are $\alpha$-stable for all allowed $\alpha >0$.
If matrices almost satisfying a group relation are close to matrices exactly satisfying the relation, then we say that a group is matricially stable. Here "almost" and "close" are in terms of the Hilbert-Schmidt norm. Using tracial 2-norm…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…