Making AI more trustworthy with a formal methods-based approach to system verification and validation.

This survey contains recent developments for computing verified results of convex constrained optimization problems, with emphasis on applications. Especially, we consider the computation of verified error bounds for non-smooth convex conic optimization in the framework of functional analysis, for linear programming, and for semidefinite programming. A discussion of important problem transforma...

This paper presents the parallelization of a self-verified method for solving dense linear equations. Verified computing provides an interval result that surely contains the correct result. The advent of parallel computing and its impact in the overall performance of various algorithms on numerical analysis have been increasing in the last decade. Two main points of this method, which demand a ...

Conventional verified methods for integration often rely on the verified bounding of analytically derived remainder formulas for popular integration rules. We show that using the approach of Taylor models, it is possible to devise new methods for verified integration of high order and in many variables. Different from conventional schemes, they do not require an a-priori derivation of analytica...

A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to compute an accurate enclosure for the Lorenz attractor. Accurately enclosing the attractor is highly relevant: a similar non verified computation is part of Tucker’s proof that the Lorenz attractor is chaotic in a rigorous mathematical sense. This proof settled a conjecture that Fields medalist Stephen Smale has put...

In spite of the fact that the effect of earthquake on earth dams has been widely studied during the past decades, the complicated behavior of such earth structures against different seismological characteristics is still unknown. Such ambiguities necessitate more accurate studies using more comprehensive computation tools to achieve new results describing the behavior of such structures subject...

In spite of the fact that the effect of earthquake on earth dams has been widely studied during the past decades, the complicated behavior of such earth structures against different seismological characteristics is still unknown. Such ambiguities necessitate more accurate studies using more comprehensive computation tools to achieve new results describing the behavior of such structures subject...