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Over-approximating (OX) program logics, such as separation logic (SL), are used for verifying properties of heap-manipulating programs: all terminating behaviour is characterised, but established results and errors need not be reachable. OX…

We present a novel modular approach to infer upper bounds on the expected runtime of probabilistic integer programs automatically. To this end, it computes bounds on the runtime of program parts and on the sizes of their variables in an…

One of the most difficult parts of motion planning in configuration space is ensuring a trajectory does not collide with task-space obstacles in the environment. Generating regions that are convex and collision free in configuration space…

In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…

Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been…

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…

This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time…

Word error rate of an ocr is often higher than its character error rate. This is especially true when ocrs are designed by recognizing characters. High word accuracies are critical to tasks like the creation of content in digital libraries…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…

Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…

We present a novel approach to differential cost analysis that, given a program revision, attempts to statically bound the difference in resource usage, or cost, between the two program versions. Differential cost analysis is particularly…

We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…

Bayesian probabilistic programming languages (BPPLs) let users denote statistical models as code while the interpreter infers the posterior distribution. The semantics of BPPLs are usually mathematically complex and unable to reason about…

The Certainty Equivalent heuristic (CE) is a widely-used algorithm for various dynamic resource allocation problems in OR and OM. Despite its popularity, existing theoretical guarantees of CE are limited to settings satisfying restrictive…

Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between of two real $n$-vectors. We derive probabilistic perturbation bounds, as well as probabilistic…

Most machine learning classifiers are designed to output posterior probabilities for the classes given the input sample. These probabilities may be used to make the categorical decision on the class of the sample; provided as input to a…

We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult…

Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving…

Phenomenon of stochastic separability was revealed and used in machine learning to correct errors of Artificial Intelligence (AI) systems and analyze AI instabilities. In high-dimensional datasets under broad assumptions each point can be…