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

On discrete groups of Euclidean isometries: representation theory, harmonic analysis and splitting properties

We study structural properties and the harmonic analysis of discrete subgroups of the Euclidean group. In particular, we 1. obtain an efficient description of their dual space, 2. develop Fourier analysis methods for periodic mappings on them, and 3. prove a Schur-Zassenhaus type splitting result

On SNF Optimization: a Functional Comparison of Methods

Abstract: In this paper we present a comparative study on methods calculating the special normal form (SNF) allowing an exact ESOP minimum representation. SNF [1] evaluation is shown to be highly practical and demonstrated results prove its real application in functional ESOP minimization and evaluation of the complexity and of the structure of Boolean functions. 1

COMPACT XOR-BI-DECOMPOSITION FOR LATTICES OF BOOLEAN FUNCTIONS

Bi-Decomposition is a powerful approach for the synthesis of multi-level combinational circuits because it utilizes the properties of the given functions to find small circuits, with low power consumption and low delay. Compact bi-decompositions restrict the variables in the support of the decomposition functions as much as possible. Methods to find compact AND-, OR-, or XOR-bi-decompositions for a given completely specified function are well known.Lattices of Boolean Functions significantly increase the possibilities to synthesize a minimal circuit. However, so far only methods to find compact AND- or OR-bidecompositions for lattices of Boolean functions are known. This gap, i.e., a method to find a compact XOR-bi-decomposition for a lattice of Boolean functions, has been closed by the approach suggested in this paper

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

Enabling Acoustic Audience Feedback in Large Virtual Events

The COVID-19 pandemic shifted many events in our daily lives into the virtual domain. While virtual conference systems provide an alternative to physical meetings, larger events require a muted audience to avoid an accumulation of background noise and distorted audio. However, performing artists strongly rely on the feedback of their audience. We propose a concept for a virtual audience framework which supports all participants with the ambience of a real audience. Audience feedback is collected locally, allowing users to express enthusiasm or discontent by selecting means such as clapping, whistling, booing, and laughter. This feedback is sent as abstract information to a virtual audience server. We broadcast the combined virtual audience feedback information to all participants, which can be synthesized as a single acoustic feedback by the client. The synthesis can be done by turning the collective audience feedback into a prompt that is fed to state-of-the-art models such as AudioGen. This way, each user hears a single acoustic feedback sound of the entire virtual event, without requiring to unmute or risk hearing distorted, unsynchronized feedback.Comment: 4 pages, 2 figure

Efficient Texture Analysis of Binary Images

A new method of determining some characteristics of binary images is proposed based on a special linear filtering. This technique enables the estimation of the area fraction, the specific line length, and the specific integral of curvature. Furthermore, the specific length of the total projection is obtained, which gives detailed information about the texture of the image. The influence of lateral and directional resolution depending on the size of the applied filter mask is discussed in detail. The technique includes a method of increasing directional resolution for texture analysis while keeping lateral resolution as high as possible