Publications

The First Tri-Lab Workshop on Formal Verification was held in Santa Fe, New Mexico, on December 5th, 2023. This workshop gathered staff from Sandia, Los Alamos, and Lawrence Livermore National Laboratories and NASA’s Jet Propulsion Laboratory. This report summarizes and expands on the presentations given and discussion had at this workshop. In this report, we describe the current capabilities and research needs related to formal methods at the NNSA labs. In particular, we identify medium-term and long-term research gaps in programming languages, formalization efforts of complex systems, embedded systems verification, hardware verification, cybersecurity, formal methods usability, workflows, numerical methods, the use of formal methods for artificial intelligence (and its converse, artificial intelligence for formal methods), and collaboration opportunities and considerations on these topics. We conclude with a small number of exemplar research problems related to these topics.

Abstract not provided.

Iterative methods for solving linear systems serve as a basic building block for computational science. The computational cost of these methods can be significantly influenced by the round-off errors that accumulate as a result of their implementation in finite precision. In the extreme case, round-off errors that occur in practice can completely prevent an implementation from satisfying the accuracy and convergence behavior prescribed by its underlying algorithm. In the exascale era where cost is paramount, a thorough and rigorous analysis of the delay of convergence due to round-off should not be ignored. In this paper, we use a small model problem and the Jacobi iterative method to demonstrate how the Coq proof assistant can be used to formally specify the floating-point behavior of iterative methods, and to rigorously prove the accuracy of these methods.