Related papers: Compiling Petri Net Mutual Reachability in Presbur…
We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…
Petri nets have found widespread use among many application domains, not least due to their human-friendly graphical syntax for the composition of interacting distributed and asynchronous processes and services, based in partial-order…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be…
Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
We consider reachability decision problems for linear dynamical systems: Given a linear map on $\mathbb{R}^d$ , together with source and target sets, determine whether there is a point in the source set whose orbit, obtained by repeatedly…
The reachability problem in cooperating systems is known to be PSPACE-complete. We show here that this problem remains PSPACE-complete when we restrict the communication structure between the subsystems in various ways. For this purpose we…
This paper deals with the reachability analysis of {P,A}-Time Petri nets ({P,A}-TPN in short) in the context of strong semantics. It investigates the convexity of the union of state classes reached by different interleavings of the same set…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
Many social networks and complex systems are found to be naturally divided into clusters of densely connected nodes, known as community structure (CS). Finding CS is one of fundamental yet challenging topics in network science. One of the…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
Timed pushdown automata (TPDA) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations of TPDA are expressible in linear arithmetic, a rich logic generalising Presburger…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
We investigate the problem of parameter synthesis for time Petri nets with a cost variable that evolves both continuously with time, and discretely when firing transitions. More precisely, parameters are rational symbolic constants used for…
Vector addition systems (VAS) constitute an important model of computation and concurrency that is equally expressive as the Petri net model. Recently, a lot of research has been conducted on vector addition systems with states (VASS),…
Vector addition system with states is an ubiquitous model of computation with extensive applications in computer science. The reachability problem for vector addition systems is central since many other problems reduce to that question. The…
Parametric timed automata (PTA) are an extension of timed automata in which clocks can be compared against parameters. The reachability problem asks for the existence of an assignment of the parameters to the non-negative integers such that…
We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric…
We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ...…
Given two families of sets $\mathcal{F}$ and $\mathcal{G}$, the $\mathcal{F}$ separability problem for $\mathcal{G}$ asks whether for two given sets $U, V \in \mathcal{G}$ there exists a set $S \in \mathcal{F}$, such that $U$ is included in…