Related papers: On Robustness for the Skolem, Positivity and Ultim…
The higher-dimensional version of Kannan and Lipton's Orbit Problem asks whether it is decidable if a target subspace can be reached from a starting point under repeated application of a linear transformation. Similarly, the continuous…
Given an integer linear recurrence sequence $\langle X_n \rangle_n$, the Skolem Problem asks to determine whether there is a natural number $n$ such that $X_n = 0$. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell…
We show that computing the strongest polynomial invariant for single-path loops with polynomial assignments is at least as hard as the Skolem problem, a famous problem whose decidability has been open for almost a century. While the…
This paper investigates a series of optimization problems for one-counter Markov decision processes (MDPs) and integer-weighted MDPs with finite state space. Specifically, it considers problems addressing termination probabilities and…
We study single-stage decision problems in which a subset of items with minimum total cost has to be selected at once from a given set of items, subject to two costs of each item -fixed and uncertain -and cardinality constraints for each…
The set of indices that correspond to the positive entries of a sequence of numbers is called its positivity set. In this paper, we study the density of the positivity set of a given linear recurrence sequence, that is the question of how…
We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. This class generalizes the class of systems with independently switching state…
Robustness is a correctness notion for concurrent programs running under relaxed consistency models. The task is to check that the relaxed behavior coincides (up to traces) with sequential consistency (SC). Although computationally simple…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
We are interested in solving decision problem $\exists? t \in \mathbb{N}, \cos t \theta = c$ where $\cos \theta$ and $c$ are algebraic numbers. We call this the $\cos t \theta$ problem. This is an exploration of Diophantine equations with…
This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…
The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether…
We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, focussing in particular on reachability, model-checking, and invariant-generation questions, both unconditionally as well as relative to…
It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…
The extension of classical imperative programs with real-valued random variables and random branching gives rise to probabilistic programs. The termination problem is one of the most fundamental liveness properties for such programs. The…
Inspired by the work of Tsiamis et al. \cite{tsiamis2022learning}, in this paper we study the statistical hardness of learning to stabilize linear time-invariant systems. Hardness is measured by the number of samples required to achieve a…