## Fachbereich Informatik

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The problem to be discussed here, is the usage of neural network clustering techniques on a mobile robot, in order to build qualitative topologic environment maps. This has to be done in realtime, i.e. the internal world model has to be adapted by the flow of sensor- samples without the possibility to stop this data-flow.Our experiments are done in a simulation environment as well as on a robot, called ALICE.

Based on the idea of using topologic feature-mapsinstead of geometric environment maps in practical mobile robot tasks, we show an applicable way tonavigate on such topologic maps. The main features regarding this kind of navigation are: handling of very inaccurate position (and orientation) information as well as implicit modelling of complex kinematics during an adaptation phase. Due to the lack of proper a-priori knowledge, a re-inforcement based model is used for the translation of navigator commands to motor actions. Instead of employing a backpropagation network for the cen-tral associative memory module (attaching actionprobabilities to sensor situations resp. navigatorcommands) a much faster dynamic cell structure system based on dynamic feature maps is shown. Standard graph-search heuristics like A* are applied in the planning phase.

Visual Search has been investigated by many researchers inspired by the biological fact, that the sensory elements on the mammal retina are not equably distributed. Therefore the focus of attention (the area of the retina with the highest density of sensory elements) has to be directed in a way to efficiently gather data according to certain criteria. The work discussed in this article concentrates on applying a laser range finder instead of a silicon retina. The laser range finder is maximal focused at any time, but therefore a low resolution total-scene-image, available with camera-like devices from scratch on, cannot be used here. By adapting a couple of algorithms, the edge-scanning module steering the laser range finder is able to trace a detected edge. Based on the data scanned so far , two questions have to be answered. First: "Should the actual (edge-) scanning be interrupted in order to give another area of interest a chance of being investigated?" and second: "Where to start a new edge-scanning, after being interrupted?". These two decision-problems might be solved by a range of decision systems. The correctness of the decisions depends widely on the actual environment and the underlying rules may not be well initialized with a-priori knowledge. So we will present a version of a reinforcement decision system together with an overall scheme for efficiently controlling highly focused devices.

ALICE
(1994)

We present a convenient notation for positive/negativeADconditional equations. Theidea is to merge rules specifying the same function by using caseAD, ifAD, matchAD, and letADexpressions.Based on the presented macroADruleADconstruct, positive/negativeADconditional equational specifiADcations can be written on a higher level. A rewrite system translates the macroADruleADconstructsinto positive/negativeADconditional equations.

This report presents a generalization of tensor-product B-spline surfaces. The new scheme permits knots whose endpoints lie in the interior of the domain rectangle of a surface. This allows local refinement of the knot structure for approximation purposes as well as modeling surfaces with local tangent or curvature discontinuities. The surfaces are represented in terms of B-spline basis functions, ensuring affine invariance, local control, the convex hull property, and evaluation by de Boor's algorithm. A dimension formula for a class of generalized tensor-product spline spaces is developed.

Termination of Rewriting
(1994)

More and more, term rewriting systems are applied in computer science aswell as in mathematics. They are based on directed equations which may be used as non-deterministic functional programs. Termination is a key property for computing with termrewriting systems.In this thesis, we deal with different classes of so-called simplification orderings which areable to prove the termination of term rewriting systems. Above all, we focus on the problemof applying these termination methods to examples occurring in practice. We introduce aformalism that allows clear representations of orderings. The power of classical simplifica-tion orderings - namely recursive path orderings, path and decomposition orderings, Knuth-Bendix orderings and polynomial orderings - is improved. Further, we restrict these orderingssuch that they are compatible with underlying AC-theories by extending well-known methodsas well as by developing new techniques. For automatically generating all these orderings,heuristic-based algorithms are given. A comparison of these orderings with respect to theirpowers and their time complexities concludes the theoretical part of this thesis. Finally, notonly a detailed statistical evaluation of examples but also a brief introduction into the designof a software tool representing the integration of the specified approaches is given.

The rapid development of any field of knowledge brings with it unavoidable fragmentation and proliferation of new disciplines. The development of computer science is no exception. Software engineering (SE) and human-computer interaction (HCI) are both relatively new disciplines of computer science. Furthermore, as both names suggest, they each have strong connections with other subjects. SE is concerned with methods and tools for general software development based on engineering principles. This discipline has its roots not only in computer science but also in a number of traditional engineering disciplines. HCI is concerned with methods and tools for the development of human-computer interfaces, assessing the usability of computer systems and with broader issues about how people interact with computers. It is based on theories about how humans process information and interact with computers, other objects and other people in the organizational and social contexts in
which computers are used. HCI draws on knowledge and skills from psychology, anthropology and sociology in addition to computer science. Both disciplines need ways of measuring how well their products and development processes fulfil their intended requirements. Traditionally SE has been concerned with 'how software is constructed' and HCI with 'how people use software'. Given the
different histories of the disciplines and their different objectives, it is not surprising that they take different approaches to measurement. Thus, each has its own distinct 'measurement culture.' In this paper we analyse the differences and the commonalties of the two cultures by examining the measurement approaches used by each. We then argue the need for a common measurement taxonomy and framework, which is derived from our analyses of the two disciplines. Next we demonstrate the usefulness of the taxonomy and framework via specific example studies drawn from our own work and that of others and show that, in fact, the two disciplines have many important similarities as well as differences and that there is some evidence to suggest that they are growing closer. Finally, we discuss the role of the taxonomy as a framework to support: reuse, planning future studies, guiding practice and facilitating communication between the two disciplines.

Optimization of Projection Methods for Solving ill-posed Problems. In this paper we propose a modification of the projection scheme for solving ill-posed problems. We show that this modification allows to obtain the best possible order of accuracy of Tikhonov Regularization using an amount of information which is far less than for the standard projection technique.

In this paper we describe a framework for defining and operationalizing conceptual models of distributed knowledge-based systems which extends published approaches by the notion of ,agents" and multiple task decompositions. The main part deals with techniques underlying our distributed interpreter. We show how a client-server-architecture can be implemented which allows prototyping distributed knowledge-based systems. Further we describe our mechanism which manages task interactions and supports dependency-directed backtracking efficiently.

Visualization of large data sets, especially on small machines, requires advanced techniques in image processing and image generation. Our hybrid raytracer is capable of rendering volumetric and geometric data simultaneously, without loss of accuracy due to data conversion. Compound data sets, consisting of several types of data, are called "hybrid data sets". There is only one rendering pipeline to obtain loss-less and efficient visualization of hybrid data. Algorithms apply to both types of data. Optical material properties are stored in the same data base for both volumetric and geometric objects, and anti-aliasing methods appeal to both data types. Stereoscopic display routines have been added to obtain true three-dimensional visualization on various media, and animation features allow generation of recordable 3-D sequences.

Free Form Volumes
(1994)

The introduction of sorts to first-order automated deduc-tion has brought greater conciseness of representation and a considerablegain in efficiency by reducing search spaces. This suggests that sort in-formation can be employed in higher-order theorem proving with similarresults. This paper develops a sorted (lambda)-calculus suitable for automatictheorem proving applications. It extends the simply typed (lambda)-calculus by ahigher-order sort concept that includes term declarations and functionalbase sorts. The term declaration mechanism studied here is powerfulenough to subsume subsorting as a derived notion and therefore gives ajustification for the special form of subsort inference. We present a set oftransformations for sorted (pre-) unification and prove the nondetermin-istic completeness of the algorithm induced by these transformations.

The main problem in computer graphics is to solve the global illumination problem,
which is given by a Fredholm integral equation of the second kind, called the radiance equation (REQ). In order to achieve realistic images, a very complex kernel
of the integral equation, modelling all physical effects of light, must be considered. Due to this complexity Monte Carlo methods seem to be an appropriate approach to solve the REQ approximately. We show that replacing Monte Carlo by quasi-Monte Carlo in some steps of the algorithm results in a faster convergence.

This paper presents fill algorithms for boundary-defined regions in raster graphics. The algorithms require only a constant size working memory. The methods presented are based on the so-called "seed fill" algorithms using the internal connectivity of the region with a given inner point. Basic methods as well as additional heuristics for speeding up the algorithm are described and verified. For different classes of regions, the time complexity of the algorithms is compared using empirical results.

Monte Carlo integration is often used for antialiasing in rendering processes.
Due to low sampling rates only expected error estimates can be stated, and the variance can be high. In this article quasi-Monte Carlo methods are presented, achieving a guaranteed upper error bound and a convergence rate essentially as fast as usual Monte Carlo.

The radiance equation, which describes the global illumination problem in computer graphics, is a high dimensional integral equation. Estimates of the solution are usually computed on the basis of Monte Carlo methods. In this paper we propose and investigate quasi-Monte Carlo methods, which means that we replace (pseudo-) random samples by low discrepancy sequences, yielding deterministic algorithms. We carry out a comparative numerical study between Monte Carlo and quasi-Monte Carlo methods. Our results show that quasi-Monte Carlo converges considerably faster.

Hardware / Software Codesign
(1994)

The Basic Reference Model of ODP introduces a number of basic concepts in order to provide a common basis for the development of a coherent set of standards. To achieve this objective, a clear understanding of the basic concepts is one prerequisite. This paper makes an effort at clarifying some of the basic concepts independently of standardized or non-standardized formal description techniques. Among the basic concepts considered here are: agent, action, interaction, interaction point, architecture, behaviour, system, composition, refinement, and abstraction. In a case study, it is then shown how these basic concepts can be represented in a formal specification written in temporal logic.

While symbolic learning approaches encode the knowledge provided by the presentation of the cases explicitly into a symbolic representation of the concept, e.g. formulas, rules, or decision trees, case-based approaches describe learned concepts implicitly by a pair (CB; d), i.e. by a set CB of cases and a distance measure d. Given the same information, symbolic as well as the case-based approach compute a classification when a new case is presented. This poses the question if there are any differences concerning the learning power of the two approaches. In this work we will study the relationship between the case base, the measure of distance, and the target concept of the learning process. To do so, we transform a simple symbolic learning algorithm (the version space algorithm) into an equivalent case-based variant. The achieved results strengthen the conjecture of the equivalence of the learning power of symbolic and casebased methods and show the interdependency between the measure used by a case-based algorithm and the target concept.

Within the present paper we investigate case-based representability as well as case-based learnability of indexed families of uniformly recursive languages. Since we are mainly interested in case-based learning with respect to an arbitrary fixed similarity measure, case-based learnability of an indexed family requires its representability, first. We show that every indexed family is case- based representable by positive and negative cases. If only positive cases are allowed the class of representable families is comparatively small. Furthermore, we present results that provide some bounds concerning the necessary size of case bases. We study, in detail, how the choice of a case selection strategy influences the learning capabilities of a case-based learner. We define different case selection strategies and compare their learning power to one another. Furthermore, we elaborate the relations to Gold-style language learning from positive and both positive and negative examples.

A method for efficiently handling associativity and commutativity (AC) in implementations of (equational) theorem provers without incorporating AC as an underlying theory will be presented. The key of substantial efficiency gains resides in a more suitable representation of permutation-equations (such as f(x,f(y,z))=f(y,f(z,x)) for instance). By representing these permutation-equations through permutations in the mathematical sense (i.e. bijective func- tions :{1,..,n} {1,..,n}), and by applying adapted and specialized inference rules, we can cope more appropriately with the fact that permutation-equations are playing a particular role. Moreover, a number of restrictions concerning application and generation of permuta- tion-equations can be found that would not be possible in this extent when treating permu- tation-equations just like any other equation. Thus, further improvements in efficiency can be achieved.

We study the complexity of local solution of Fredholm integral equations. This means that we want to compute not the full solution, but rather a functional (weighted mean, value in a point) of it. For certain Sobolev classes of multivariate periodic functions we prove matching upper and lower bounds and construct an algorithm of the optimal order, based on Fourier coefficients and a hyperbolic cross approximation.

In this paper the complexity of the local solution of Fredholm integral equations
is studied. For certain Sobolev classes of multivariate periodic functions with dominating mixed derivative we prove matching lower and upper bounds. The lower bound is shown using relations to s-numbers. The upper bound is proved in a constructive way providing an implementable algorithm of optimal order based on Fourier coefficients and a hyperbolic cross approximation.

Best-Fit Pattern Matching
(1994)

This report shows that dispatching of methods in object oriented languages is in principle the same as best fit pattern matching. A general conceptual description of best fit pattern matching is presented. Many object oriented features are modelled by means of the general concept. This shows that simple methods, multi methods, overloading of functions, pattern matching,
dynamic and union types, and extendable records can be combined in a single comprehensive concept.

Automatic proof systems are becoming more and more powerful.However, the proofs generated by these systems are not met withwide acceptance, because they are presented in a way inappropriatefor human understanding.In this paper we pursue two different, but related, aims. First wedescribe methods to structure and transform equational proofs in away that they conform to human reading conventions. We developalgorithms to impose a hierarchical structure on proof protocols fromcompletion based proof systems and to generate equational chainsfrom them.Our second aim is to demonstrate the difficulties of obtaining suchprotocols from distributed proof systems and to present our solutionto these problems for provers using the TEAMWORK method. Wealso show that proof systems using this method can give considerablehelp in structuring the proof listing in a way analogous to humanbehaviour.In addition to theoretical results we also include descriptions onalgorithms, implementation notes, examples and data on a variety ofexamples.

The problem to interpolate Hermite-type data (i.e. two points with attached tangent vectors) with elastic curves of prescribed tension is known to have multiple solutions. A method is presented that finds all solutions of length not exceeding one period of its curvature function. The algorithm is based on algebraic relations between discrete curvature information which allow to transform the problem into a univariate one. The method operates with curves that by construction partially interpolate the given data. Hereby the objective function of the problem is drastically simplified. A bound on the maximum curvature value is established that provides an interval containing all solutions.

We introduce the concept of streamballs for fluid flow visualization. Streamballs are based upon implicit surface generation techniques adopted from the well-known metaballs. Their property to split or merge automatically in areas of significant divergence or convergence makes them an ideal tool for the visualization of arbitrary complex flow fields. Using convolution surfaces generated by continuous skeletons for streamball construction offers the possibility to visualize even tensor fields.

A Case Study on Specifikation,Detection and Resolution of IN Feature Interactions with Estelle
(1994)

We present an approach for the treatment of Feature Interactions in Intelligent Networks. The approach is based on the formal description technique Estelle and consists of three steps. For the first step, a specification style supporting the integration of additional features into a basic service is introduced . As a result, feature integration is achieved by adding specification text, i.e . on a purely syntactical level. The second step is the detection of feature interactions resulting from the integration of additional features. A formal criterion is given that can be used for the automatic detection of a particular class of feature interactions. In the third step, previously detected feature interactions are resolved. An algorithm has been devised that allows the automatical incorporation of high-level design decisions into the formal specification. The presented approach is applied to the Basic Call Service and several supplementary interacting features.