Related papers: (Un)Solvable Loop Analysis
We consider the problem of establishing that a program-synthesis problem is unrealizable (i.e., has no solution in a given search space of programs). Prior work on unrealizability has developed some automatic techniques to establish that a…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…
Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…
This study covers an analytical approach to calculate positively invariant sets of dynamical systems. Using Lyapunov techniques and quantifier elimination methods, an automatic procedure for determining bounds in the state space as an…
We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
We present a framework to decompose real multivariate polynomials while preserving invariance and positivity. This framework has been recently introduced for tensor decompositions, in particular for quantum many-body systems. Here we…
An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit…
We propose a novel framework of program and invariant synthesis called neural network-guided synthesis. We first show that, by suitably designing and training neural networks, we can extract logical formulas over integers from the weights…
This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a PCTL…
We show that the emptiness (unsatisfiability) problem is undecidable and $\mathrm{\Pi}^{0}_{1}$-complete for deterministic propositional while programs with (graph) loop. To this end, we introduce a hypothesis elimination using loops. Using…
Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We describe the Aligator.jl software package for automatically generating all polynomial invariants of the rich class of extended P-solvable loops with nested conditionals. Aligator.jl is written in the programming language Julia and is…
We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
In this paper, we present an approach for fault-tolerant synthesis by combining predefined patterns for fault-tolerance with algorithmic game solving. A non-fault-tolerant system, together with the relevant fault hypothesis and…