The Solution of SAT Problems Using Ternary Vectors and Parallel Processing

This paper will show a new approach to the solution of SAT-problems. It has been based on the isomorphism between the Boolean algebras of finite sets and the Boolean algebras of logic functions depending on a finite number of binary variables. Ternary vectors are the main data structure representing sets of Boolean vectors. The respective set operations (mainly the complement and the intersection) can be executed in a bit-parallel way (64 bits at present), but additionally also on different processors working in parallel. Even a hierarchy of processors, a small set of processor cores of a single CPU, and the huge number of cores of the GPU has been taken into consideration. There is no need for any search algorithms. The approach always finds all solutions of the problem without consideration of special cases (such us no solution, one solution, all solutions). It also allows to include problem-relevant knowledge into the problem-solving process at an early point of time. Very often it is possible to use ternary vectors directly for the modeling of a problem. Some examples are used to illustrate the efficiency of this approach (Sudoku, Queen's problems on the chessboard, node bases in graphs, graph-coloring problems, Hamiltonian and Eulerian paths etc.)

Earthquake classifying neural networks trained with random dynamic neighborhood PSOs

This paper investigates the use of Random Dynamic Neighborhoods in Particle Swarm Optimization (PSO) for the purpose of training fixed-architecture neural networks to classify a real-world data set of seismological data. Instead of the ring or fully-connected neighborhoods that are typically used with PSOs, or even more complex graph structures, this work uses directed graphs that are randomly generated using size and uniform out-degree as parameters. Furthermore, the graphs are subjected to dynamism during the course of a run, thereby allowing for varying information exchange patterns. Neighborhood re-structuring is applied with a linearly decreasing probability at each iteration. Several experimental configurations are tested on a training portion of the data set, and are ranked according to their abilities to generalize over the entire set. Comparisons are performed with standard PSOs as well as several static non-random neighborhoods.Arvind S. Mohais, Rosemarie Mohais, Christopher Ward and Christian Posthof

Algorithmisches Lernen fuer wissensbasierte Systeme Abschlussbericht

Evaluations of decisions (in a wide sense) play a dominant role in the development and the use of knowledge-based systems. They are a main topic in knowledge acquisition. Therefore, the topic of the project 'Learning of Evaluation Functions' has been considered in a general kind of view. Classical evaluation functions have a lot of shortcomings. Therefore, alternative approaches for further investigations have been suggested: 1. The concept of diagnosis, 2. The logical approach, 3. The knowledge-based approach, 4. The fuzzy-logic approach. While running this project these four approaches had been investigated more detailed. This report contains the essential results of the project. It consists of three parts. Part A discusses the approaches 1 to 3 theoretically. Part B shows that the existence of optimal strategies is a decisive condition for objective evaluations. Therefrom a solution for handling diagnosis is derived. Finally, Part C investigates the fuzzy-logic approach in search algorithms. (orig.)SIGLEAvailable from TIB Hannover: F95B219+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Forschung und Technologie (BMFT), Bonn (Germany)DEGerman

Nonstandard Concepts of Similarity in Case-Based Reasoning

Introduction The present paper is aimed at propagating new concepts of similarity more flexible and expressive than those underlying most case-based reasoning approaches today. So, it mainly deals with criticizing approaches in use, with motivating and introducing new notions and notations, and with first steps towards future applications. The investigations at hand originate from the author's work in learning theory. In exploring the relationship between inductive learning and case-based learning within a quite formal setting (cf. [Jan92b]), it turned out that both areas almost coincide, if sufficiently flexible similarity concepts are taken into acount. This provides some formal arguments for the necessity of non-symmetric similarity measures. Encouraged by these first results, the author tried to investigate more structured learning problems from the view point of case-based reasoning. It turned out that an appropriate handling requires formalisms allowing similarity conce