Related papers: Reachability in Vector Addition Systems is Ackerma…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. We introduce and study…
This study focuses on reachability problems in differential games. An improved level set method for computing reachable tubes is proposed in this paper. The reachable tube is described as a sublevel set of a value function, which is the…
A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graph where the edges are labeled with different types of opening and closing parentheses, and the reachability information is computed…
This paper presents Verisig, a hybrid system approach to verifying safety properties of closed-loop systems using neural networks as controllers. Although techniques exist for verifying input/output properties of the neural network itself,…
Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the…
Node-connectivity augmentation is a fundamental network design problem. We are given a $k$-node connected graph $G$ together with an additional set of links, and the goal is to add a cheap subset of links to $G$ to make it $(k+1)$-node…
We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): the problem of finding a mapping of a request graph (describing a workload) onto a substrate graph (describing the physical…
Solving a singular linear system for an individual vector solution is an ill-posed problem with a condition number infinity. From an alternative perspective, however, the general solution of a singular system is of a bounded sensitivity as…
In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…
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…
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…
Reachability logic has been applied to $\mathbb{K}$ rewrite-rule-based language definitions as a language-generic logic of programs. To be able to verify not just code but also distributed system designs, a new rewrite-theory-generic…
We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
The Steiner Tree problem is a classical problem in combinatorial optimization: the goal is to connect a set $T$ of terminals in a graph $G$ by a tree of minimum size. Karpinski and Zelikovsky (1996) studied the $\delta$-dense version of…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
The Distance Geometry Problem asks for a realization of a given weighted graph in $\mathbb{R}^K$. Two variants of this problem, both originating from protein conformation, are based on a given vertex order (which abstracts the protein…
In this work, we present a novel Koopman spectrum-based reachability verification method for nonlinear systems. Contrary to conventional methods that focus on characterizing all potential states of a dynamical system over a presupposed time…