Related papers: Fine-grained reductions around CFL-reachability
In this column, we overview recent progress by many authors on understanding the approximability of constraint satisfaction problems (CSPs) in low-space streaming models. Inspired by this recent progress, we collate nine conjectural lower…
Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…
The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify their behavior and guarantee safety. This paper presents a backward reachability approach for safety verification of neural…
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…
Safety filters based on Control Barrier Functions (CBFs) provide formal guarantees of forward invariance, but are often difficult to implement in networked dynamical systems. This is due to global coupling and communication requirements.…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We present an algorithm for data-driven reachability analysis that estimates finite-horizon forward reachable sets for general nonlinear systems using level sets of a certain class of polynomials known as Christoffel functions. The level…
The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial…
We present a novel feasibility criteria for the finite intersection of convex sets given by inequalities. This criteria allows us to easily assert the feasibility by analyzing the unconstrained minimum of a speci?fic convex function, that…
Reachability for piecewise affine systems is known to be undecidable, starting from dimension $2$. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…
The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations…
In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point…
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
We show how to reduce a general, strictly-feasible LP problem, into a min-max problem, which can be solved by the algorithm from the third section of my thesis.
In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial time, even if the digraph has multiple edges. We also show a…
Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…
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…
Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…