Related papers: On the Completeness and Ordering of Path-Complete …
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
We establish a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. At the center of this framework lies the concept of a $\leqslant$-parametric graph:…
This paper presents a formalism for defining properties of paths in graph databases, which can be used to restrict the number of solutions to navigational queries. In particular, our formalism allows us to define quantitative properties…
Provable safety is one of the most critical challenges in automated driving. The behavior of numerous traffic participants in a scene cannot be predicted reliably due to complex interdependencies and the indiscriminate behavior of humans.…
This work explores a collaborative method for ensuring safety in multi-agent formation control problems. We formulate a control barrier function (CBF) based safety filter control law for a generic distributed formation controller and extend…
We report on intermediate results of -- to the best of our knowledge -- the first study of completeness thresholds for (partially) bounded memory safety proofs. Specifically, we consider heap-manipulating programs that iterate over arrays…
This paper addresses the challenge of ensuring safety and feasibility in control systems using Control Barrier Functions (CBFs). Existing CBF-based Quadratic Programs (CBF-QPs) often encounter feasibility issues due to mixed relative degree…
The software system under test can be modeled as a graph comprising of a set of vertices, (V) and a set of edges, (E). Test Cases are Test Paths over the graph meeting a particular test criterion. In this paper, we present a method to…
This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the \emph{robust} case, in which the…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs.…
Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.
The safety of mobile robots in dynamic environments is predicated on making sure that they do not collide with obstacles. In support of such safety arguments, we analyze and formally verify a series of increasingly powerful safety…
The theory of combinatorial designs has recently been used in order to build switch-centric data centre networks incorporating a large number of servers, in comparison with the popular Fat-Tree data centre network. The construction…
Reasoning paths are reliable information in knowledge graph completion (KGC) in which algorithms can find strong clues of the actual relation between entities. However, in real-world applications, it is difficult to guarantee that…
In this paper we give an overview of results on the analysis of parametric linear hybrid automata, and of systems of similar linear hybrid automata: We present possibilities of describing systems with a parametric (i.e. not explicitly…
This paper is motivated by controllers developed for autonomous vehicles which occasionally result into conditions where safety is no longer guaranteed. We develop an exact-time safety recovery framework for any control-affine nonlinear…
A full-homomorphism between a pair of graphs is a vertex mapping that preserves adjacencies and non-adjacencies. For a fixed graph $H$, a full $H$-colouring is a full-homomorphism of $G$ to $H$. A minimal $H$-obstruction is a graph that…
Optimization-based safety filters, such as control barrier function (CBF) based quadratic programs (QPs), have demonstrated success in controlling autonomous systems to achieve complex goals. These CBF-QPs can be shown to be continuous, but…
We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…