Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.Comment: No. RR-7826 (2011

Propagating Torsion in 3D-Gravity and Dynamical Mass Generation

In this paper, fermions are minimally coupled to 3D-gravity where a dynamical torsion is introduced. A Kalb-Ramond field is non-minimally coupled to these fermions in a gauge-invariant way. We show that a 1-loop mass generation mechanism takes place for both the 2-form gauge field and the torsion. As for the fermions, no mass is dynamically generated: at 1-loop, there is only a mass shift proportional to the Yukawa coupling whenever the fermions have a non-vanishing tree-level mass.Comment: 13 pages, latex file, no figures, some corrections adde

Symmetry aspects of fermions coupled to torsion and electromagnetic fields

We study and explore the symmetry properties of fermions coupled to dynamical torsion and electromagnetic fields. The stability of the theory upon radiative corrections as well as the presence of anomalies are investigated.Comment: 9 pages, LaTe

A Formally Verified Floating-Point Implementation of the Compact Position Reporting Algorithm

The Automatic Dependent Surveillance-Broadcast (ADS-B) system allows aircraft to communicate their current state, including position and velocity information, to other aircraft in their vicinity and to ground stations. The Compact Position Reporting (CPR) algorithm is the ADS-B module responsible for the encoding and decoding of aircraft positions. CPR is highly sensitive to computer arithmetic since it heavily relies on functions that are intrinsically unstable such as floor and modulo. In this paper, a formally-verified double-precision floating-point implementation of the CPR algorithm is presented. The verification proceeds in three steps. First, an alternative version of CPR, which reduces the floating-point rounding error is proposed. Then, the Prototype Verification System (PVS) is used to formally prove that the ideal real-number counterpart of the improved algorithm is mathematically equivalent to the standard CPR definition. Finally, the static analyzer Frama-C is used to verify that the double-precision implementation of the improved algorithm is correct with respect to its operational requirement. The alternative algorithm is currently being considered for inclusion in the revised version of the ADS-B standards document as the reference implementation of the CPR algorithm

Vector Supersymmetry of 2D Yang-Mills Theory

The vector supersymmetry of the 2D topological BF model is extended to 2D Yang-Mills. The consequences of the corresponding Ward identity on the ultraviolet behavior of the theory are analyzed.Comment: Some references adde

A Fistful of Dollars: Formalizing Asymptotic Complexity Claims via Deductive Program Verification

Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018International audienceWe present a framework for simultaneously verifying the functional correctness and the worst-case asymptotic time complexity of higher-order imperative programs. We build on top of Separation Logic with Time Credits, embedded in an interactive proof assistant. We formalize the O notation, which is key to enabling modular specifications and proofs. We cover the subtleties of the multivariate case, where the complexity of a program fragment depends on multiple parameters. We propose a way of integrating complexity bounds into specifications, present lemmas and tactics that support a natural reasoning style, and illustrate their use with a collection of examples

Discussing Quantum Aspects of Higher-Derivative 3D-Gravity in the First-Order Formalism

In this paper, we reassess the issue of deriving the propagators and identifying the spectrum of excitations associated to the vielbein and spin connection of (1+2)-D gravity in the presence of dynamical torsion, while working in the first-order formulation. A number of peculiarities is pointed out whenever the Chern-Simons term is taken into account along with a combination of bilinear terms in the torsion tensor. We present a procedure to derive the full set of propagators, based on an algebra of enlarged spin-type operators, and we discuss under which conditions the poles of the tree-level 2-point functions correspond to physical excitations that do not conflict with causality and unitarity

The Apheis project: Air Pollution and Health—A European Information System

At a time when the Health Effects Institute, Centers for Disease Control, and Environmental Protection Agency are creating an Environmental Public Health Tracking Program on Air Pollution Effects in the USA, it seemed useful to share the experience acquired since 1999 by the Apheis project (Air Pollution and Health—A European Information System), which has tracked the effects of air pollution on health in 26 European cities and continues to do so as the new Aphekom project. In particular, this paper first describes the continuing impact of air pollution on health in Europe, how the Apheis project came to be and evolved, what its main objectives and achievements have been, and how the project benefited its participants. The paper then summarizes the main learnings of the Apheis project

On the static solutions in gravity with massive scalar field in three dimensions

We investigate circularly symmetric static solutions in three-dimensional gravity with a minimally coupled massive scalar field. We integrate numerically the field equations assuming asymptotic flatness, where black holes do not exist and a naked singularity is present. We also give a brief review on the massless cases with cosmological constant.Comment: 11 pages, LaTeX, 1 Postscript figure. Some changes were don

Supersymmetric Extension of the Lorentz and CPT-Violating Maxwell-Chern-Simons Model

Focusing on gauge degrees of freedom specified by a 1+3 dimensions model hosting a Maxwell term plus a Lorentz and CPT non-invariant Chern-Simons-like contribution, we obtain a minimal extension of such a system to a supersymmetric environment. We comment on resulting peculiar self-couplings for the gauge sector, as well as on background contribution for gaugino masses. Furthermore, a non-polynomial generalization is presented.Comment: revtex4, 4 pages, no figure