Related papers: Affine Extensions of Integer Vector Addition Syste…

The problem of reliable communication over the multiple-access channel (MAC) with states is investigated. We propose a new coding scheme for this problem which uses quasi-group codes (QGC). We derive a new computable single-letter…

We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…

Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using…

This paper tackles the problem of the existence of solutions for recursive systems of Horn clauses with second-order variables interpreted as integer relations, and harnessed by quantifier-free difference bounds arithmetic. We start by…

We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…

This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…

An MSTD set is a finite set of integers with more sums than differences. It is proved that, for infinitely many positive integers $k$, there are infinitely many affinely inequivalent MSTD sets of cardinality $k$. There are several related…

To every Banach space V we associate a compact right topological affine semigroup E(V). We show that a separable Banach space V is Asplund if and only if E(V) is metrizable, and it is Rosenthal (i.e. it does not contain an isomorphic copy…

This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available.…

We consider two basic problems of algebraic topology, the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given…

We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation…

Approximate Message Passing (AMP) algorithms provide a valuable tool for studying mean-field approximations and dynamics in a variety of applications. Although these algorithms are often first derived for matrices having independent…

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…

Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…

We present an approach to parameterized reachability for communicating finite-state threads that formulates the analysis as a satisfiability problem. In addition to the unbounded number of threads, the main challenge for SAT/SMT-based…

We introduce a novel architecture and computational framework for formal, automated analysis of systems with a broad set of nonlinearities in the feedback loop, such as neural networks, vision controllers, switched systems, and even simple…

We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability…

This paper addresses a fundamental challenge in data-driven reachability analysis: accurately representing and propagating non-convex reachable sets. We propose a novel approach using constrained polynomial zonotopes to describe reachable…

This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a…

We study fair distribution of a collection of m indivisible goods among a group of n agents, using the widely recognized fairness principles of Maximin Share (MMS) and Any Price Share (APS). These principles have undergone thorough…