Related papers: Certificates for Probabilistic Pushdown Automata v…

Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…

Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful…

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…

Rare-event simulation techniques, such as importance sampling (IS), constitute powerful tools to speed up challenging estimation of rare catastrophic events. These techniques often leverage the knowledge and analysis on underlying system…

Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…

When Perturbation Analysis (PA) yields unbiased sensitivity estimators for expected-value performance functions in discrete event dynamic systems, it can be used for performance optimization of those functions. However, when PA is known to…

Probabilistic rounding error analysis can yield much sharper bounds than classical worst-case theory, but existing results typically rely on zero-mean rounding errors and often leave the confidence parameter implicit. This work revisits…

Many works in convex optimization provide rates for achieving a small primal gap. However, this quantity is typically unavailable in practice. In this work, we show that solving a regularized surrogate with algorithms based on simple…

Polyhedra form an established abstract domain for inferring runtime properties of programs using abstract interpretation. Computations on them need to be certified for the whole static analysis results to be trusted. In this work, we look…

Estimating the probability of failure is an important step in the certification of safety-critical systems. Efficient estimation methods are often needed due to the challenges posed by high-dimensional input spaces, risky test scenarios,…

This paper presents an empirical study regarding training probabilistic neural networks using training objectives derived from PAC-Bayes bounds. In the context of probabilistic neural networks, the output of training is a probability…

Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…

In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…

We consider the problem of minimizing a polynomial $f$ over the binary hypercube. We show that, for a specific set of polynomials, their binary non-negativity can be checked in a polynomial time via minimum cut algorithms, and we construct…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function that guarantees a desired property. However, algorithms for…

Stability guarantees have emerged as a principled way to evaluate feature attributions, but existing certification methods rely on heavily smoothed classifiers and often produce conservative guarantees. To address these limitations, we…

The probabilistic bisection algorithm (PBA) solves a class of stochastic root-finding problems in one dimension by successively updating a prior belief on the location of the root based on noisy responses to queries at chosen points. The…

Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. Among all valid confidence sets for…

Safety in stochastic control systems, which are subject to random noise with a known probability distribution, aims to compute policies that satisfy predefined operational constraints with high confidence throughout the uncertain evolution…