A Simple Numeric Set-Theoretical Method of the Logic Differential Calculus

Предложен новый метод логического дифференциального исчисления на основании числового теоретико-множественного подхода к определению разных типов логических производных произвольного порядка от булевой функции. Алгоритм имеет относительно меньшую вычислительную сложность при меньшем количестве операций, необходимых для решения задачи, что подтверждено примерами определения разных логических производных произвольных порядков от функций, заимствованных авторами из известных публикаций в порядке сравнения с предложенным методом.Запропоновано новий метод логічного диференційного числення на основі числового теоретико-множинного підходу до визначення різних типів логічних похідних довільного порядку від бульової функції. Алгоритм має відносно меншу обчислювальну складність за меншої кількості операцій, необхідних для розв'язання задачі, що підтверджено прикладами визначення запропонованим методом різних логічних похідних довільних порядків від функцій, запозичених авторами з відомих публікацій з метою порівняння з пропонованим методом.A new method of the logic differential calculus, based on the numeric set-theoretical approach for the definition of the different logic derivatives types of the arbitrary order for Boolean function is proposed. The given algorithm has relatively less computational complexity due to the lower amount of the operations required for solving the given problem. This is proved in the given examples borrowed from the well-known publications, in order to compare them with the proposed numeric set-theoretic method to obtain the different types of logic derivatives of arbitrary order

A survey of an introduction to fault diagnosis algorithms

This report surveys the field of diagnosis and introduces some of the key algorithms and heuristics currently in use. Fault diagnosis is an important and a rapidly growing discipline. This is important in the design of self-repairable computers because the present diagnosis resolution of its fault-tolerant computer is limited to a functional unit or processor. Better resolution is necessary before failed units can become partially reuseable. The approach that holds the greatest promise is that of resident microdiagnostics; however, that presupposes a microprogrammable architecture for the computer being self-diagnosed. The presentation is tutorial and contains examples. An extensive bibliography of some 220 entries is included

Separating codes and traffic monitoring

International audienceThis paper studies the problem of traffic monitoring which consists of differentiating a set of walks on a directed graph by placing sensors on as few arcs as possible. The problem of characterising a set of individuals by testing as few attributes as possible is already well-known, but traffic monitoring presents new challenges that the previous models of separation fall short from modelling such as taking into account the multiplicity and order of the arcs in a walk. We introduce a new and stronger model of separation based on languages that generalises the traffic monitoring problem. We study three subproblems with practical applications and develop methods to solve them by combining integer linear programming, separating codes and language theory

Single fault detection in combinational logic circuits

The material in this paper is divided into the following four chapters for convenience. Chapter 1 explains, how the idea of fault testing changed from testing the machine instructions to testing the hardware in logic circuits. Chapters 2, 3 and 4 present the different approaches considered, namely: 1. Path sensitizing and D-Algorithm method. 2. Tabular method. 3. Boolean difference method