Combinational multiple-valued circuit design by generalised disjunctive decomposition

A design of multiple-valued circuits based on the multiple-valued programmable logic arrays (MV PLA’s) by generalized disjunctive decomposition is presented. Main subjects are 1) Generalized disjunctive decomposition of multiple-valued functions using multiple-terminal multiplevalued decision diagrams (MTMDD’s); 2) Realization of functions by MV PLA-based combinatorial circuits

Genetic algorithm approach to find the best input variable partitioning

Conference PaperThis paper presents a variable partition algorithm which combines the quasi-reduced ordered multiple-terminal multiple-valued decision diagrams and genetic algorithms (GAs). The algorithm is better than the previous techniques which find a good functional decomposition by non-exhaustive search and expands the range of searching for the best decomposition providing the optimal subtable multiplicity. The possible solutions are evaluated using the gain of decomposition for a multiple-output multiple-valued logic function. The distinct feature of GA is the possible solutions being coded by real numbers. Here the simplex-based crossover is proposed to use for the recombination stage of GA. It permits to increase the GA coverag

Time complexity analysis of generalized decomposition algorithm

The time complexity of the fast algorithm for generalized disjunctive decomposition of an rvalued function is studied.The considered algorithm to find the best decomposition is based on the analysis of multiple-terminal multiple-valued decision diagrams. It is shown that the time complexity for random rvalued functions depends on the such restriction as the number n1 of inputs in the first level circuit. In the case where the best partition of input variables is searched with restriction the time complexity is reduced in several times. The algorithm was simulated on a digital computer. The experimental results are in agreement with the theoretical predictions

Using a genetic algorithm for optimizing the functional decomposition of multiple-valued functions

The genetic algorithm which determines the good functional decomposition of multiple-valued logic functions is presented. The algorithm expands the range of searching for a best decomposition, providing the optimal column multiplicity. The possible solutions are evaluated using the gain of decomposition for multiple-valued function

Recognizing Decomposition of a Partial Boolean Function

A hard combinatorial problem is investigated which has useful application in design of discrete devices: the two-block decomposition of a partial Boolean function. The key task is regarded: finding such a weak partition on the set of arguments, at which the considered function can be decomposed. Solving that task is essentially speeded up by the way of preliminary discovering traces of the sought-for partition. Efficient combinatorial operations are used by that, based on parallel execution of operations above adjacent units in the Boolean space

Conditionally Optimal Algorithms for Generalized B\"uchi Games

Games on graphs provide the appropriate framework to study several central problems in computer science, such as the verification and synthesis of reactive systems. One of the most basic objectives for games on graphs is the liveness (or B\"uchi) objective that given a target set of vertices requires that some vertex in the target set is visited infinitely often. We study generalized B\"uchi objectives (i.e., conjunction of liveness objectives), and implications between two generalized B\"uchi objectives (known as GR(1) objectives), that arise in numerous applications in computer-aided verification. We present improved algorithms and conditional super-linear lower bounds based on widely believed assumptions about the complexity of (A1) combinatorial Boolean matrix multiplication and (A2) CNF-SAT. We consider graph games with $n$ vertices, $m$ edges, and generalized B\"uchi objectives with $k$ conjunctions. First, we present an algorithm with running time $O(k \cdot n^2)$, improving the previously known $O(k \cdot n \cdot m)$ and $O(k^2 \cdot n^2)$ worst-case bounds. Our algorithm is optimal for dense graphs under (A1). Second, we show that the basic algorithm for the problem is optimal for sparse graphs when the target sets have constant size under (A2). Finally, we consider GR(1) objectives, with $k_1$ conjunctions in the antecedent and $k_2$ conjunctions in the consequent, and present an $O(k_1 \cdot k_2 \cdot n^{2.5})$-time algorithm, improving the previously known $O(k_1 \cdot k_2 \cdot n \cdot m)$-time algorithm for $m > n^{1.5}$

Global Optimisation for Energy System

The goal of global optimisation is to find globally optimal solutions, avoiding local optima and other stationary points. The aim of this thesis is to provide more efficient global optimisation tools for energy systems planning and operation. Due to the ongoing increasing of complexity and decentralisation of power systems, the use of advanced mathematical techniques that produce reliable solutions becomes necessary. The task of developing such methods is complicated by the fact that most energy-related problems are nonconvex due to the nonlinear Alternating Current Power Flow equations and the existence of discrete elements. In some cases, the computational challenges arising from the presence of non-convexities can be tackled by relaxing the definition of convexity and identifying classes of problems that can be solved to global optimality by polynomial time algorithms. One such property is known as invexity and is defined by every stationary point of a problem being a global optimum. This thesis investigates how the relation between the objective function and the structure of the feasible set is connected to invexity and presents necessary conditions for invexity in the general case and necessary and sufficient conditions for problems with two degrees of freedom. However, nonconvex problems often do not possess any provable convenient properties, and specialised methods are necessary for providing global optimality guarantees. A widely used technique is solving convex relaxations in order to find a bound on the optimal solution. Semidefinite Programming relaxations can provide good quality bounds, but they suffer from a lack of scalability. We tackle this issue by proposing an algorithm that combines decomposition and linearisation approaches. In addition to continuous non-convexities, many problems in Energy Systems model discrete decisions and are expressed as mixed-integer nonlinear programs (MINLPs). The formulation of a MINLP is of significant importance since it affects the quality of dual bounds. In this thesis we investigate algebraic characterisations of on/off constraints and develop a strengthened version of the Quadratic Convex relaxation of the Optimal Transmission Switching problem. All presented methods were implemented in mathematical modelling and optimisation frameworks PowerTools and Gravity

Framework for sustainable TVET-Teacher Education Program in Malaysia Public Universities

Studies had stated that less attention was given to the education aspect, such as teaching and learning in planning for improving the TVET system. Due to the 21st Century context, the current paradigm of teaching for the TVET educators also has been reported to be fatal and need to be shifted. All these disadvantages reported hindering the country from achieving the 5th strategy in the Strategic Plan for Vocational Education Transformation to transform TVET system as a whole. Therefore, this study aims to develop a framework for sustainable TVET Teacher Education program in Malaysia. This study had adopted an Exploratory Sequential Mix-Method design, which involves a semi-structured interview (phase one) and survey method (phase two). Nine experts had involved in phase one chosen by using Purposive Sampling Technique. As in phase two, 118 TVET-TE program lecturers were selected as the survey sample chosen through random sampling method. After data analysis in phase one (thematic analysis) and phase two (Principal Component Analysis), eight domains and 22 elements have been identified for the framework for sustainable TVET-TE program in Malaysia. This framework was identified to embed the elements of 21st Century Education, thus filling the gap in this research. The research findings also indicate that the developed framework was unidimensional and valid for the development and research regarding TVET-TE program in Malaysia. Lastly, it is in the hope that this research can be a guide for the nations in producing a quality TVET teacher in the future