Related papers: Small Universal Petri Nets with Inhibitor Arcs
We propose a new method that takes advantage of structural reductions to accelerate the verification of reachability properties on Petri nets. Our approach relies on a state space abstraction, called polyhedral abstraction, which involves a…
This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and…
Recent work has proposed neural network pruning techniques to reduce the size of a network while preserving robustness against adversarial examples, i.e., well-crafted inputs inducing a misclassification. These methods, which we refer to as…
Time-Basic Petri nets, is a powerful formalism for modeling real-time systems where time constraints are expressed through time functions of marking's time description associated with transition, representing possible firing times. We…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
We study the size and the complexity of computing finite state automata (FSA) representing and approximating the downward and the upward closure of Petri net languages with coverability as the acceptance condition. We show how to construct…
The complexity of highly interconnected systems is rooted in the interwoven architecture defined by its connectivity structure. In this paper, we develop matrix energy of the underlying connectivity structure as a measure of topological…
Being able to find small Petri nets with the same behaviour as formal specifications of concurrent systems benefits both effective verification and practical implementation of such systems. This paper considers specifications given in the…
An important parameter in a secret sharing scheme is the number of minimal qualified sets. Given this number, the universal access structure is the richest possible structure, namely the one in which there are one or more participants in…
The purpose of this document is to provide data about known Betti numbers of unordered configuration spaces of small graphs in order to guide research and avoid duplicated effort. It contains information for connected multigraphs having at…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
Cutwidth is one of the classic layout parameters for graphs. It measures how well one can order the vertices of a graph in a linear manner, so that the maximum number of edges between any prefix and its complement suffix is minimized. As…
The verification of safety properties for concurrent systems often reduces to the coverability problem for Petri nets. This problem was shown to be ExpSpace-complete forty years ago. Driven by the concurrency revolution, it has regained a…
A new graph-based order parameter is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system, and is transferable to all structural geometries. Three sets of data are…
A graph is sub-unicyclic if it contains at most one cycle. We also say that a graph $G$ is $k$-apex sub-unicyclic if it can become sub-unicyclic by removing $k$ of its vertices. We identify 29 graphs that are the minor-obstructions of the…
In this paper, we address sorting networks that are constructed from comparators of arity $k > 2$. That is, in our setting the arity of the comparators -- or, in other words, the number of inputs that can be sorted at the unit cost -- is a…
We study simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal possible Betti numbers. We find that these simplicial complexes have very special combinatorial and topological structures. For…
In this note we study the computational complexity of feedback arc set counting problems in directed graphs, highlighting some subtle yet common properties of counting classes. Counting the number of feedback arc sets of cardinality $k$ and…
We improve the best known upper bound on the number of edges in a unit-distance graph on $n$ vertices for each $n\in\{16,\ldots,30\}$. When $n\leq 21$, our bounds match the best known lower bounds, and we fully enumerate the densest…
We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…