Платформенно-независимая спецификация и верификация стандартной математической функции квадратного корня

The project “Platform-independent approach to formal specification and verification of standard mathematical functions” is aimed onto the development of incremental combined approach to specification and verification of standard Mathematical functions like sqrt, cos, sin, etc. Platform-independence means that we attempt to design a relatively simple axiomatization of the computer arithmetics in terms of real arithmetics (i.e. the field $\mathbb{R}$ of real numbers) but do not specify neither base of the computer arithmetics, nor a format of numbers representation. Incrementality means that we start with the most straightforward specification of the simplest case to verify the algorithm in real numbers and finish with a realistic specification and a verification of the algorithm in computer arithmetics. We call our approach combined because we start with manual (pen-and-paper) verification of the algorithm in real numbers, then use this verification as proof-outlines for a manual verification of the algorithm in computer arithmetics, and finish with a computer-aided validation of the manual proofs with a proof-assistant system (to avoid appeals to “obviousness” that are common in human-carried proofs). In the paper, we apply our platform-independent incremental combined approach to specification and verification of the standard Mathematical square root function. Currently a computer-aided validation was carried for correctness (consistency) of our fix-point arithmetics and for the existence of a look-up table with the initial approximations of the square roots for fix-point numbers.Цель проекта “Платформенно-независимый подход к формальной спецификации и верификации стандартных математических функций” --- инкрементальный комбинированный подход к спецификации и верификации стандартных математических функций, таких как sqrt, cos, sin и так далее. Платформенно-независимый подход предполагает простую аксиоматизацию машинной арифметики в терминах вещественной арифметики (то есть арифметики поля $\mathbb{R}$ вещественных чисел), не фиксируя ни основание системы счисления, ни формат машинного слова. Инкрементальность означает, что спецификация и верификация начинается с рассмотрения наиболее “простого” случая – элементарной спецификации и верификации простого алгоритма, работающего с вещественными числами, а заканчивается модификацией элементарной спецификации и алгоритма для машинной арифметики и верификацией алгоритма, работающего в машинной арифметике. А комбинированность подхода означает, что мы начинаем с рассмотрения “базового случая” --- “ручной” верификации (с ручкой и бумагой) для алгоритма, работающего в вещественной арифметике, затем выполняем ручную верификацию алгоритма, работающего в машинной арифметике, используя верификацию для базового случая в качестве “конспекта” (proof-outlines), а заканчиваем --- верификацией с использованием автоматизированной системы построения/поиска доказательства для того, чтобы исключить апелляцию к “очевидности” в ручной верификации. В статье платформенно-независимый инкрементальный комбинированный подход применяется для спецификации и верификации стандартной математической функции квадратного корня. В настоящий момент автоматизированная верификация разработанных алгоритмов выполнена только частично: с использованием системы ACL2 доказана реализуемость (существование) чисел с фиксированной запятой и таблицы начальных приближений квадратного корня

Small scale software engineering

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In computing, the Software Crisis has arisen because software projects cannot meet their planned timescales, functional capabilities, reliability levels and budgets. This thesis reduces the general problem down to the Small Scale Software Engineering goal of improving the quality and tractability of the designs of individual programs. It is demonstrated that the application of eight abstractions (set, sequence, hierarchy, h-reduction, integration, induction, enumeration, generation) can lead to a reduction in the size and complexity of and an increase in the quality of software designs when expressed via Dimensional Design, a new representational technique which uses the three spatial dimensions to represent set, sequence and hierarchy, whilst special symbols and axioms encode the other abstractions. Dimensional Designs are trees of symbols whose edges perceptually encode the relationships between the nodal symbols. They are easy to draw and manipulate both manually and mechanically. Details are given of real software projects already undertaken using Dimensional Design. Its tool kit, DD/ROOTS, produces high quality, machine drawn, detailed design documentation plus novel quality control information. A run time monitor records and animates execution, measures CPU time and takes snapshots etc; all these results are represented according to Dimensional Design principles to maintain conceptual integrity with the design. These techniques are illustrated by the development of a non-trivial example program. Dimensional Design is axiomatised, compared to existing techniques and evaluated against the stated problem. It has advantages over existing techniques, mainly its clarity of expression and ease of manipulation of individual abstractions due to its graphical basis

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Techniques for the realization of ultrareliable spaceborne computers Interim scientific report

Error-free ultrareliable spaceborne computer

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions