BOOLEAN DIFFERENTIAL EQUATIONS - A COMMON MODEL FOR CLASSES, LATTICES, AND ARBITRARY SETS OF BOOLEAN FUNCTIONS

The Boolean Differential Calculus (BDC) significantly extends the Boolean Algebra because not only Boolean values 0 and 1, but also changes of Boolean valuesor Boolean functions can be described. A Boolean Differential Equation (BDE)is a Boolean equation that includes derivative operations of the Boolean Differential Calculus. This paper aims at the classification of BDEs, the characterization of the respective solutions, algorithms to calculate the solution of a BDE, and selected applications. We will show that not only classes and arbitrary sets of Boolean functions but also lattices of Boolean functions can be expressed by Boolean Differential Equations.In order to reach this aim, we give a short introduction into the BDC, emphasizethe general difference between the solutions of a Boolean equation and a BDE, explain the core algorithms to solve a BDE that is restricted to all vectorial derivatives of f(x) and optionally the Boolean variables. We explain formulas for transforming other derivative operations to vectorial derivatives in order to solve more general BDEs. New fields of applications for BDEs are simple and generalized lattices of Boolean functions. We describe the construction, simplification and solution.The basic operations of XBOOLE are sufficient to solve BDEs. We demonstratehow a XBOOLE-problem program (PRP) of the freely available XBOOLE-Monitorquickly solves some BDEs

Sturm-Lıouvılle Problems And Boolean Dıfferentıal Equatıons

This thesis consists of five sections. In the first section, the important points of subject which we studied are introduced. In the second section, the biological diffu- sion process is examined with mathematical model and the solution by method of separation variables. Formulation of the general Sturm-Liouville problem is given in the third section. In the fourth section, main results on Sturm-Liouville problem is given with important properties. In addition to the properties, boundary value problem and Green’s function is introduced and relation between Green’s function and regular Sturm-Liouville problem via eigenfunction expansion is given. After giving the important theorems, completeness of eigenfunctions of Sturm-Liouville problems are investigated in the fourth section of the thesis. In the final section, Boolean Differential Equations which are very important in Mathematical Logic are introduced. The purpose of this section is to start to investigate getting Boolean form of Sturm-Liouville problems if it is possible.Bu tez bes bölümden olusmaktadır. Birinci bölümde, çalıstığımız konunun önemli noktaları tanıtıldı. İkinci bölümde, biyolojiksel difüzyon sürecinin matematiksel modeli ve değiskenlerine ayrılabilir yöntemi çalısıldı. Sturm-Liouville probleminin formülü üçüncü bölümde ve ana sonuçları ile önemli özellikleri ise dördüncü bölümde verildi. Özelliklere ek olarak, sınır değer problemi ile Green fonksiyonu tanıldı ve özfonksiyon açılımı yardımıyla olan Sturm-Liouville problemi ve Green fonksiyonu arasındaki iliski anlatıldı. Yine dördüncü bölümde, önemli teoremler verildikten sonra, Sturm-Liouville problemlerinin özfonksiyonlarının tamlığı arastırıldı. Final bölümünde, Matematiksel Lojik’te çok önemli bir yer tutan Boolean Diferansiyel Denklemleri tanıtıldı. Bu bölüm, eğer varsa, Sturm-Liouville problemlerinin Boolean formunu arastırmak için bir ön adım niteliğini tasımaktadır

Mixed-level identification of fault redundancy in microprocessors

A new high-level implementation independent functional fault model for control faults in microprocessors is introduced. The fault model is based on the instruction set, and is specified as a set of data constraints to be satisfied by test data generation. We show that the high-level test, which satisfies these data constraints, will be sufficient to guarantee the detection of all non-redundant low level faults. The paper proposes a simple and fast simulation based method of generating test data, which satisfy the constraints prescribed by the proposed fault model, and a method of evaluating the high-level control fault coverage for the proposed fault model and for the given test. A method is presented for identification of the high-level redundant faults, and it is shown that a test, which provides 100% coverage of non-redundant high-level faults, will also guarantee 100% non-redundant SAF coverage, whereas all gate-level SAF not covered by the test are identified as redundant. Experimental results of test generation for the execution part of a microprocessor support the results presented in the paper.Comment: 2019 IEEE Latin American Test Symposium (LATS

Parallel Solution of Covering Problems Super-Linear Speedup on a Small Set of Cores

This paper aims at better possibilities to solveproblems of exponential complexity. Our special focus is thecombination of the computational power of four cores of astandard PC with better approaches in the application domain.As the main example we selected the unate covering problemwhich must be solved, among others, in the process of circuitsynthesis and for graph-covering (domination) problems.We introduce into the wide field of problems that can besolved using Boolean models. We explain the models and theclassic solutions, and discuss the results of a selected model byusing a benchmark set. Subsequently we study sources of parallelismin the application domain and explore improvementsgiven by the parallel utilization of the available four cores ofa PC. Starting with a uniform splitting of the problem, wesuggest improvements by means of an adaptive division andan intelligent master. Our experimental results confirm thatthe combination of improvements of the application modelsand of the algorithmic domain leads to a remarkable speedupand an overall improvement factor of more than 35 millionsin comparison with the improved basic approach

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

Decomposition tool targeting FPGA architectures

The growing interest in the field of logic synthesis targeting Field Programmable Gate Arrays (FPGA) and the active research carried out by a number of research groups in the area of functional decomposition is the prime motivation for this thesis. Logic synthesis has been an area of interest in many universities all over the world. The work involves the study and implementation of techniques and methods in logic synthesis. In this work, a logic synthesis tool has been developed implementing the aspects of general and complete Decomposition method based on functional decomposition techniques [4]. The tool is aimed at producing outputs faster and more efficient than the available software. C++ Standard template library is used to develop this tool. The output of this tool is designed to be compatible with the available vendor software. The tool has been tested on MCNC benchmarks and those created keeping in mind the industry requirements

Chemical process control : present status and future needs ; the view from European industry

Not only in Europe, chemical process control is characterized by a broad invasion of distributed control systems into chemical plants. The information integration from process control up to business management is a great challenge of today which follows from the overall computerization of production. Most of the recent progress in process automation results from the application of computer science paradigms to control systems, and of advanced developments in field instrumentation. Despite these advances and the considerable progress made in process control theory, there is only limited acceptance and application of modern advanced process control methodologies in industrial practice. This paper is an attempt to summarize the European discussion on the reasons for these facts

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue