Bernd Steinbach

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 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.

Extremely Complex 4-Colored Rectangle-Free Grids: Solution of Open Multiple-Valued Problems

This paper aims at the rectangle-free coloring of grids using four colors. It has been proven in a well developed theory that there is an upper bound of rectangle-free 4-colorable grids as well as a lower bound of grids for which no rectangle-free color pattern of four colors exist. Between these tight bounds the grids of the size 17×17, 17×18, 18 × 17, and 18 ×18 are located for which it is not known until now whether a rectangle-free coloring by four colors exists. We present in this paper an approach that solves all these open problems. From another point of view this paper aims at the solution of a multiple-valued problem having an extremely high complexity. There are 1.16798 * 10195 different grids of four colors. It must be detected whether at least one of this hardly imaginable large number of patterns satisfies strong additional conditions. In order to solve this highly complex problem, several approaches were taken into account to find out properties of the problem which finally allowed us to calculate the solution.

Bi-decomposition of function sets in multiple-valued logic for circuit design and data mining

This article presents a theory for the bi-decomposition of functions in multi-valued logic (MVL). MVL functions are applied in logic design of multi-valued circuits and machine learning applications. Bi-decomposition is a method to decompose a function into two decomposition functions that are connected by a two-input operator called gate. Each of the decomposition functions depends on fewer variables than the original function. Recursive bi-decomposition represents a function as a structure of interconnected gates. For logic synthesis, the type of the gate can be chosen so that it has an efficient hardware representation. For machine learning, gates are selected to represent simple and understandable classification rules.Algorithms are presented for non-disjoint bi-decomposition, where the decomposition functions may share variables with each other. Bi-decomposition is discussed for the min- and max-operators. To describe the MVL bi-decomposition theory, the notion of incompletely specified functions is generalized to function intervals. The application of MVL differential calculus leads to particular efficient algorithms. To ensure complete recursive decomposition, separation is introduced as a new concept to simplify non-decomposable functions. Multi-decomposition is presented as an example of separation.The decomposition algorithms are implemented in a decomposition system called YADE. MVL test functions from logic synthesis and machine learning applications are decomposed. The results are compared to other decomposers. It is verified that YADE finds decompositions of superior quality by bi-decomposition of MVL function sets.

Bi-decompositions of multi-valued functions for circuit design and data mining applications

We present efficient algorithms for the bi-decomposition of arbitrary incompletely specified functions in variable-valued logic. Several special cases are discussed. The algorithms are especially applicable for Data Mining applications, because, in contrast to the general multi-valued approaches to function decomposition that decompose to arbitrary tables, we create a network from multi-valued two-input operators that are selected by the user. Such decompositions lead to decision rules that are easier to understand by humans.

Improvements of the construction of exact minimal covers of boolean functions

The calculation of an exact minimal cover of a Boolean function is an NP-complete problem. In this paper we introduce the definition of this problem and its basic solution. By using a slightly modified algorithm, we get a speed-up factor of more than 104. The main contributions of this paper are the description of an alternative approach mentioned in [15], and a remarkable improvement of this algorithm. In both cases operations of the XBOOLE library are used. Using the newly suggested algorithm, the time required for the calculation could be reduced by a factor of more than 8∗108 in comparison with the previous algorithm.

Decomposition of multi-valued functions into min- and max-gates

This paper presents algorithms that allow the realization of multi-valued functions as a multi-level network consisting of min- and max-gates. The algorithms are based on bi-decomposition of function intervals, a generalization of incompletely specified functions. Multi-valued derivation operators are applied to compute decomposition structures. For validation the algorithms have been implemented in the YADE system. Results of the decomposition of functions from machine learning applications are listed and compared to the results of another decomposer.

Exploiting Functional Properties of Boolean Functions for Optimal Multi-Level Design by Bi-Decomposition

This paper introduces the theory of bi-decomposition of Boolean functions. This approach optimally exploits functional properties of a Boolean function in order to find an associated multilevel circuit representation having a very short delay by using simple two input gates. The machine learning process is based on the Boolean Differential Calculus and is focused on the aim of detecting the profitable functional properties availablefor the Boolean function.For clear understanding the bi-decomposition of completely specifiedBoolean functions is introduced first. Significantly better chance of successare given for bi-decomposition of incompletely specifiedBoolean functions, discussed secondly. The inclusion of the weak bi-decomposition allows to prove the the completeness of the suggested decomposition method. The basic task for machine learning consists of determining the decomposition type and dedicated sets of variables. Lean on this knowledge a complete recursive design algorithm is suggested.Experimental results over MCNC benchmarks show that the bi-decomposition outperforms SIS and other BDD-based decomposition methods interms of area and delay of the resulting circuits with comparableCPU time.By switching from the ON-set/OFF-set model of Boolean function lattices to their upper- and lower-bound model a new view to the bi-decomposition arises. This new form of the bi-decomposition theorymakes a comprehensible generalization of the bi-decomposition to multivalued function possible.

Several approaches to parallel computing in the Boolean domain

Each additional variable doubles the number of function values of a Boolean function. This exponential increase is known as combinational explosion and limits strongly the solvable problems for a given computer. In order to solve larger Boolean problems, it is necessary to exploit each concept that reduces the required efforts. The parallel consideration of all Boolean variables that are assigned to a machine word of the computer, the mapping of an exponential number of Boolean vectors to a single ternary vector, and the distribution of the calculations to several Boolean spaces are some approaches which were realized in the software package XBOOLE. An important further approach is the segmentation of the Boolean tasks and their parallel computation using several connected computers as well as the available processor cores of these computers. In this paper we explore alternative approaches to parallel computations of Boolean problems. Experimental results document the achieved benefits.

Logic Functions and Equations

We will introduce now one of the core concepts — logic functions. We want to draw the attention of the reader to the fact that many other names are used synonymously, like switching functions, binary functions, Boolean functions, constraints, truth functions etc. It is always important to check the given definitions and to find out which names are used in a given context.

UML-based co-design for run-time reconfigurable architectures

In this article we present an object-oriented approach and a development environment for the system-level design of run-time reconfigurable computer systems. We use the Unified Modelling Language (UML) for the specification, modelling, documentation, and visualization throughout all phases of development, from specification to synthesis. The proposed approach is based on hardware-software co-design and Model Driven Architecture (MDA). This way we allow for thorough and complete system representations, platform-independence, comprehensible and seamless transition from specification to implementation, and the description of common development artifacts and activities. In this article we will focus on aspects and problems which are related to object-orientation, UML, and MDA.