Abstract

Abstract

Abstract

Abstract
With the incresasing importance of program verification, an issue that has been receiving more attention is the certification of verification tools, addressing the vernacular question: Who verifies the verifier?. In this paper we approach this meta-verification problem by focusing on a fundamental component of program verifiers: the Verification Conditions Generator (VCGen), responsible for producing a set of proof obligations from a program and a specification. The semantic foundations of VCGens lie in program logics, such as Hoare logic, Dynamic logic, or Separation logic, and related predicate transformers. Dynamic logic is the basis of the KeY system, one of the foremost deductive verifiers, whose logic makes use of the notion of update, which is quite intricate to formalize. In this paper we derive systematically, based on a KeY-style dynamic logic, a correct-by-construction VCGen for a toy programming language. Our workflow covers the entire process, from the logic to the VCGen. It is implemented in the Why3 tool, which is itself a program verifier. We prove the soundness and (an appropriate notion of) completeness of the logic, then define a VCGen for our language and establish its soundness. Dynamic logic is one of a variety of research topics that our dear friend and colleague Luis Soares Barbosa has, over the years, initiated and promoted at the University of Minho. It is a pleasure for us to dedicate this work to him on the occasion of his 60th birthday.

Abstract
Symptoms-based detection of SARS-CoV-2 infection is not a substitute for precise diagnostic tests but can provide insight into the likely level of infection in a given population. This study uses symptoms data collected in the Global COVID-19 Trends and Impact Surveys (UMD Global CTIS), and data on variants sequencing from GISAID. This work, conducted in January of 2022 during the emergence of the Omicron variant (subvariant BA.1), aims to improve the quality of infection detection from the available symptoms and to use the resulting estimates of infection levels to assess the changes in vaccine efficacy during a change of dominant variant; from the Delta dominant to the Omicron dominant period. Our approach produced a new symptoms-based classifier, Random Forest, that was compared to a ground-truth subset of cases with known diagnostic test status. This classifier was compared with other competing classifiers and shown to exhibit an increased performance with respect to the ground-truth data. Using the Random Forest classifier, and knowing the vaccination status of the subjects, we then proceeded to analyse the evolution of vaccine efficacy towards infection during different periods, geographies and dominant variants. In South Africa, where the first significant wave of Omicron occurred, a significant reduction of vaccine efficacy is observed from August-September 2021 to December 2021. For instance, the efficacy drops from 0.81 to 0.30 for those vaccinated with 2 doses (of Pfizer/BioNTech), and from 0.51 to 0.09 for those vaccinated with one dose (of Pfizer/BioNTech or Johnson & Johnson). We also extended the study to other countries in which Omicron has been detected, comparing the situation in October 2021 (before Omicron) with that of December 2021. While the reduction measured is smaller than in South Africa, we still found, for instance, an average drop in vaccine efficacy from 0.53 to 0.45 among those vaccinated with two doses. Moreover, we found a significant negative (Pearson) correlation of around - 0.6 between the measured prevalence of Omicron in several countries and the vaccine efficacy in those same countries. This prediction, in January of 2022, of the decreased vaccine efficacy towards Omicron is in line with the subsequent increase of Omicron infections in the first half of 2022.