Related papers: Flattability of Priority Vector Addition Systems
We study the approximability of the four-vertex model, a special case of the six-vertex model.We prove that, despite being NP-hard to approximate in the worst case, the four-vertex model admits a fully polynomial randomized approximation…
Scheduling is a key decision-making process to improve the performance of flexible manufacturing systems. Place-timed Petri nets provide a formal method for graphically modeling and analyzing such systems. By generating reachability graphs…
This study aims at characterizing a reachable set of a hybrid dynamical system with a lag constraint in the switch control. The setting does not consider any controllability assumptions and uses a level-set approach. The approach consists…
In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets…
Coverability in Petri nets finds applications in verification of safety properties of reactive systems. We study coverability in the equivalent model: Vector Addition Systems with States (VASS). A k-VASS can be seen as k counters and a…
Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms \cite{llr},…
Variational Learning (VL) has recently gained popularity for training deep neural networks. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but little…
Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the…
A complete characterization of the complexity of the reachability problem for vector addition system has been open for a long time. The problem is shown to be Tower complete.
Vector addition systems are an important model in theoretical computer science and have been used for the analysis of systems in a variety of areas. Termination is a crucial property of vector addition systems and has received considerable…
We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence,…
We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors of a stacked system are unitarily equivalent to a product of…
The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper,…
We study detectability properties for labeled Petri nets and finite automata. We first study weak approximate detectability (WAD) that implies that there exists an infinite observed output sequence of the system such that each prefix of the…
In this paper we consider the reachability problem for bounded branching VASS. Bounded VASS are a variant of the classic VASS model where all values in all configurations are upper bounded by a fixed natural number, encoded in binary in the…
We study the synthesis of inductive half spaces (IHS). These are linear inequalities that form inductive invariants for Petri nets, capable of disproving reachability or coverability. IHS generalize classic notions of invariants like traps…
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,…
In many kinds of infinite-state systems, the coverability problem has significantly lower complexity than the reachability problem. In order to delineate the border of computational hardness between coverability and reachability, we propose…
A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would…
In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's…