Reliability and reproducibility of Atlas information

We discuss the reliability and reproducibility of much of the information contained in the Atlas of Finite Groups

Formal Verification of Real-Time Function Blocks Using PVS

A critical step towards certifying safety-critical systems is to check their conformance to hard real-time requirements. A promising way to achieve this is by building the systems from pre-verified components and verifying their correctness in a compositional manner. We previously reported a formal approach to verifying function blocks (FBs) using tabular expressions and the PVS proof assistant. By applying our approach to the IEC 61131-3 standard of Programmable Logic Controllers (PLCs), we constructed a repository of precise specification and reusable (proven) theorems of feasibility and correctness for FBs. However, we previously did not apply our approach to verify FBs against timing requirements, since IEC 61131-3 does not define composite FBs built from timers. In this paper, based on our experience in the nuclear domain, we conduct two realistic case studies, consisting of the software requirements and the proposed FB implementations for two subsystems of an industrial control system. The implementations are built from IEC 61131-3 FBs, including the on-delay timer. We find issues during the verification process and suggest solutions.Comment: In Proceedings ESSS 2015, arXiv:1506.0325

Tight asteroseismic constraints on core overshooting and diffusive mixing in the slowly rotating pulsating B8.3V star KIC 10526294

KIC 10526294 is a very slowly rotating and slowly pulsating late B-type star. Its 19 consecutive dipole gravity modes constitute a series with almost constant period spacing. This unique collection of identified modes probes the near-core environment of this star and holds the potential to reveal the size and structure of the overshooting zone on top of the convective core, as well as the mixing properties of the star. We pursue forward seismic modelling based on adiabatic eigenfrequencies of equilibrium models for eight extensive evolutionary grids tuned to KIC 10526294, by varying the initial mass, metallicity, chemical mixture, and the extent of the overshooting layer on top of the convective core. We examine models for both OP and OPAL opacities and test the occurrence of extra diffusive mixing. We find a tight mass, metallicity relation within the ranges $M$ ~ 3.13 to 3.25 Msun and $Z$ ~ 0.014 to 0.028. We deduce that an exponentially decaying diffusive core overshooting prescription describes the seismic data better than a step function formulation and derive a value of $f_{ov}$ between 0.017 and 0.018. Moreover, the inclusion of extra diffusive mixing with a value of $\log D_{\rm mix}$ between 1.75 and 2.00 dex (with $D_{\rm mix}$ in cm^2/sec) improves the goodness-of-fit based on the observed and modelled frequencies with a factor 11 compared to the case where no extra mixing is considered, irrespective of the $(M,Z)$ combination within the allowed seismic range. The inclusion of diffusive mixing in addition to core overshooting is essential to explain the structure in the observed period spacing pattern of this star. Moreover, we deduce that an exponentially decaying prescription for the core overshooting is to be preferred over a step function. Our best models for KIC 10526294 approach the seismic data to a level that they can serve future inversion of its stellar structure.Comment: 13 pages, 4 tables, 12 figures, accepted for publication in Astronomy & Astrophyic

Carnap: an Open Framework for Formal Reasoning in the Browser

This paper presents an overview of Carnap, a free and open framework for the development of formal reasoning applications. Carnap’s design emphasizes flexibility, extensibility, and rapid prototyping. Carnap-based applications are written in Haskell, but can be compiled to JavaScript to run in standard web browsers. This combination of features makes Carnap ideally suited for educational applications, where ease-of-use is crucial for students and adaptability to different teaching strategies and classroom needs is crucial for instructors. The paper describes Carnap’s implementation, along with its current and projected pedagogical applications