Related papers: On the Completeness and Ordering of Path-Complete …
Flip graphs of non-crossing configurations in the plane are widely studied objects, e.g., flip graph of triangulations, spanning trees, Hamiltonian cycles, and perfect matchings. Typically, it is an easy exercise to prove connectivity of a…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time…
Safety is of paramount importance in control systems to avoid costly risks and catastrophic damages. The control barrier function (CBF) method, a promising solution for safety-critical control, poses a new challenge of enhancing control…
Safety requirements in dynamical systems are commonly enforced with set invariance constraints over a safe region of the state space. Control barrier functions, which are Lyapunov-like functions for guaranteeing set invariance, are an…
Recent advances in Deep Machine Learning have shown promise in solving complex perception and control loops via methods such as reinforcement and imitation learning. However, guaranteeing safety for such learned deep policies has been a…
Given a set of obstacles and two points, is there a path between the two points that does not cross more than $k$ different obstacles? This is a fundamental problem that has undergone a tremendous amount of work. It is known to be NP-hard,…
This paper introduces control barrier functions for discrete-time systems, which can be shown to be necessary and sufficient for controlled invariance of a given set. Moreover, we propose nonlinear discrete-time control barrier functions…
We present an algorithm for planning trajectories that avoid obstacles and satisfy key-door precedence specifications expressed with a fragment of signal temporal logic. Our method includes a novel exact convex partitioning of the obstacle…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…
We survey the state-of-the-art on model-based formalisms for safety and security joint analysis, where safety refers to the absence of unintended failures, and security to absence of malicious attacks. We conduct a thorough literature…
Planning safe motions for legged robots requires sophisticated safety verification tools. However, designing such tools for such complex systems is challenging due to the nonlinear and high-dimensional nature of these systems' dynamics. In…
Achieving safe autonomous navigation systems is critical for deploying robots in dynamic and uncertain real-world environments. In this paper, we propose a hierarchical control framework leveraging neural network verification techniques to…
The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov processes and associated boundaries, analysis of path-space,…
Connected automated vehicles have shown great potential to improve the efficiency of transportation systems in terms of passenger comfort, fuel economy, stability of driving behavior and mitigation of traffic congestions. Yet, to deploy…
A Hamiltonian path (a Hamiltonian cycle) in a graph is a path (a cycle, respectively) that traverses all of its vertices. The problems of deciding their existence in an input graph are well-known to be NP-complete, in fact, they belong to…
Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance…
In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the…
Control barrier functions are a popular method of ensuring system safety, and these functions can be used to enforce invariance of a set under the dynamics of a system. A control barrier function must have certain properties, and one must…
Autonomous vehicles face tremendous challenges while interacting with human drivers in different kinds of scenarios. Developing control methods with safety guarantees while performing interactions with uncertainty is an ongoing research…