## Fachbereich Informatik

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- Case Based Reasoning (2)
- Case-Based Reasoning (1)
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World models for mobile robots as introduced in many projects, are mostly redundant regarding similar situations detected in different places. The present paper proposes a method for dynamic generation of a minimal world model based on these redundancies. The technique is an extention of the qualitative topologic world modelling methods. As a central aspect the reliability regarding errortolerance and stability will be emphasized. The proposed technique demands very low constraints on the kind and quality of the employed sensors as well as for the kinematic precision of the utilized mobile platform. Hard realtime constraints can be handled due to the low computational complexity. The principal discussions are supported by real-world experiments with the mobile robot "

We describe a hybrid case-based reasoning system supporting process planning for machining workpieces. It integrates specialized domain dependent reasoners, a feature-based CAD system and domain independent planning. The overall architecture is built on top of CAPlan, a partial-order nonlinear planner. To use episodic problem solving knowledge for both optimizing plan execution costs and minimizing search the case-based control component CAPlan/CbC has been implemented that allows incremental acquisition and reuse of strategical problem solving experience by storing solved problems as cases and reusing them in similar situations. For effective retrieval of cases CAPlan/CbC combines domain-independent and domain-specific retrieval mechanisms that are based on the hierarchical domain model and problem representation.

Structured domains are characterized by the fact that there is an intrinsic dependency between certain key elements in the domain. Considering these dependencies leads to better performance of the planning systems, and it is an important factor for determining the relevance of the cases stored in a case-base. However, testing for cases that meet these dependencies, decreases the performance of case-based planning, as other criterions need also to be consider for determining this relevance. We present a domain-independent architecture that explicitly represents these dependencies so that retrieving relevant cases is ensured without negatively affecting the performance of the case-based planning process.

Correctness and runtime efficiency are essential properties of software ingeneral and of high-speed protocols in particular. Establishing correctnessrequires the use of FDTs during protocol design, and to prove the protocolcode correct with respect to its formal specification. Another approach toboost confidence in the correctness of the implementation is to generateprotocol code automatically from the specification. However, the runtimeefficiency of this code is often insufficient. This has turned out to be amajor obstacle to the use of FDTs in practice.One of the FDTs currently applied to communication protocols is Es-telle. We show how runtime efficiency can be significantly improved byseveral measures carried out during the design, implementation and run-time of a protocol. Recent results of improvements in the efficiency ofEstelle-based protocol implementations are extended and interpreted.

We describe a hybrid architecture supporting planning for machining workpieces. The architecture is built around CAPlan, a partial-order nonlinear planner that represents the plan already generated and allows external control decision made by special purpose programs or by the user. To make planning more efficient, the domain is hierarchically modelled. Based on this hierarchical representation, a case-based control component has been realized that allows incremental acquisition of control knowledge by storing solved problems and reusing them in similar situations.

Evaluation is an important issue for every scientific field and a necessity for an emerging soft-ware technology like case- based reasoning. This paper is a supplementation to the review of industrial case-based reasoning tools by K.-D. Althoff, E. Auriol, R. Barletta and M. Manago which describes the most detailed evaluation of commercial case-based reasoning tools currently available. The author focuses on some important aspects that correspond to the evaluation ofcase-based reasoning systems and gives links to ongoing research.

Case-Based Reasoning for Decision Support and Diagnostic Problem Solving: The INRECA Approach
(1995)

INRECA offers tools and methods for developing, validating, and maintaining decision support systems. INRECA's basic technologies are inductive and case-based reasoning, namely KATE -INDUCTION (cf., e.g., Manago, 1989; Manago, 1990) and S3-CASE, a software product based on PATDEX (cf., e.g., Wess,1991; Richter & Wess, 1991; Althoff & Wess, 1991). Induction extracts decision knowledge from case databases. It brings to light patterns among cases and helps monitoring trends over time. Case-based rea -soning relates the engineer's current problem to past experiences.

Self-localization in unknown environments respectively correlation of current and former impressions of the world is an essential ability for most mobile robots. The method,proposed in this article is the construction of a qualitative, topological world model as a basis for self-localization. As a central aspect the reliability regarding error-tolerance and stability will be emphasized. The proposed techniques demand very low constraints for the kind and quality of the employed sensors as well as for the kinematic precisionof the utilized mobile platform. Hard real-time constraints can be handled due to the low computational complexity. The principal discussions are supported by real-world experiments with the mobile robot.

In this paper the autonomous mobile vehicle MOBOT-IV is presented, which is capable of exploring an indoor-environment while building up an internal representation of its world. This internal model is used for the navigation of the vehicle during and after the exploration phase. In contrast to methods, which use a grid based or line based environment representation, in the approach presented in this paper, local sector maps are the basic data structure of the world model. This paper describes the method of the view-point-planning for map building, the use of this map for navigation and the method of external position estimation including the hand- ling of an position error in a moving real-time system.

The well-known and powerful proof principle by well-founded induction says that for verifying \(\forall x : P (x)\) for some property \(P\) it suffices to show \(\forall x : [[\forall y < x :P (y)] \Rightarrow P (x)] \) , provided \(<\) is a well-founded partial ordering on the domainof interest. Here we investigate a more general formulation of this proof principlewhich allows for a kind of parameterized partial orderings \(<_x\) which naturallyarises in some cases. More precisely, we develop conditions under which theparameterized proof principle \(\forall x : [[\forall y <_x x : P (y)] \Rightarrow P (x)]\) is sound in thesense that \(\forall x : [[\forall y <_x x : P (y)] \Rightarrow P (x)] \Rightarrow \forall x : P (x)\) holds, and givecounterexamples demonstrating that these conditions are indeed essential.

We study the combination of the following already known ideas for showing confluence ofunconditional or conditional term rewriting systems into practically more useful confluence criteria forconditional systems: Our syntactic separation into constructor and non-constructor symbols, Huet's intro-duction and Toyama's generalization of parallel closedness for non-noetherian unconditional systems, theuse of shallow confluence for proving confluence of noetherian and non-noetherian conditional systems, theidea that certain kinds of limited confluence can be assumed for checking the fulfilledness or infeasibilityof the conditions of conditional critical pairs, and the idea that (when termination is given) only primesuperpositions have to be considered and certain normalization restrictions can be applied for the sub-stitutions fulfilling the conditions of conditional critical pairs. Besides combining and improving alreadyknown methods, we present the following new ideas and results: We strengthen the criterion for overlayjoinable noetherian systems, and, by using the expressiveness of our syntactic separation into constructorand non-constructor symbols, we are able to present criteria for level confluence that are not criteria forshallow confluence actually and also able to weaken the severe requirement of normality (stiffened withleft-linearity) in the criteria for shallow confluence of noetherian and non-noetherian conditional systems tothe easily satisfied requirement of quasi-normality. Finally, the whole paper also gives a practically usefuloverview of the syntactic means for showing confluence of conditional term rewriting systems.

We present a method for learning heuristics employed by an automated proverto control its inference machine. The hub of the method is the adaptation of theparameters of a heuristic. Adaptation is accomplished by a genetic algorithm.The necessary guidance during the learning process is provided by a proof prob-lem and a proof of it found in the past. The objective of learning consists infinding a parameter configuration that avoids redundant effort w.r.t. this prob-lem and the particular proof of it. A heuristic learned (adapted) this way canthen be applied profitably when searching for a proof of a similar problem. So,our method can be used to train a proof heuristic for a class of similar problems.A number of experiments (with an automated prover for purely equationallogic) show that adapted heuristics are not only able to speed up enormously thesearch for the proof learned during adaptation. They also reduce redundancies inthe search for proofs of similar theorems. This not only results in finding proofsfaster, but also enables the prover to prove theorems it could not handle before.

The feature interaction problem in telecommunications systems increasingly ob-structs the evolution of such systems. We develop formal detection criteria whichrender a necessary (but less than sufficient) condition for feature interactions. It can be checked mechanically and points out all potentially critical spots. Thesehave to be analysed manually. The resulting resolution decisions are incorporatedformally. Some prototype tool support is already available. A prerequisite forformal criteria is a formal definition of the problem. Since the notions of featureand feature interaction are often used in a rather fuzzy way, we attempt a formaldefinition first and discuss which aspects can be included in a formalization (andtherefore in a detection method). This paper describes ongoing work.

In dieser Dissertation wird das Konzept der Gröbnerbasen für endlich erzeugte Monoid-und Gruppenringe verallgemeinert. Dabei werden Reduktionsmethoden sowohl zurDarstellung der Monoid- beziehungsweise Gruppenelemente, als auch zur Beschreibungder Rechtsidealkongruenz in den entsprechenden Monoid- beziehungsweise Gruppenrin-gen benutzt. Da im allgemeinen Monoide und insbesondere Gruppen keine zulässigenOrdnungen mehr erlauben, treten bei der Definition einer geeigneten Reduktionsrela-tion wesentliche Probleme auf: Zum einen ist es schwierig, die Terminierung einer Re-duktionsrelation zu garantieren, zum anderen sind Reduktionsschritte nicht mehr mitMultiplikationen verträglich und daher beschreiben Reduktionen nicht mehr unbedingteine Rechtsidealkongruenz. In dieser Arbeit werden verschiedene Möglichkeiten Reduk-tionsrelationen zu definieren aufgezeigt und im Hinblick auf die beschriebenen Problemeuntersucht. Dabei wird das Konzept der Saturierung, d.h. eine Polynommenge so zu er-weitern, daß man die von ihr erzeugte Rechtsidealkongruenz durch Reduktion erfassenkann, benutzt, um Charakterisierungen von Gröbnerbasen bezüglich der verschiedenenReduktionen durch s-Polynome zu geben. Mithilfe dieser Konzepte ist es gelungenfür spezielle Klassen von Monoiden, wie z.B. endliche, kommutative oder freie, undverschiedene Klassen von Gruppen, wie z.B. endliche, freie, plain, kontext-freie odernilpotente, unter Ausnutzung struktureller Eigenschaften spezielle Reduktionsrelatio-nen zu definieren und terminierende Algorithmen zur Berechnung von Gröbnerbasenbezüglich dieser Reduktionsrelationen zu entwickeln.

Problems stemming from the study of logic calculi in connection with an infer-ence rule called "condensed detachment" are widely acknowledged as prominenttest sets for automated deduction systems and their search guiding heuristics. Itis in the light of these problems that we demonstrate the power of heuristics thatmake use of past proof experience with numerous experiments.We present two such heuristics. The first heuristic attempts to re-enact aproof of a proof problem found in the past in a flexible way in order to find a proofof a similar problem. The second heuristic employs "features" in connection withpast proof experience to prune the search space. Both these heuristics not onlyallow for substantial speed-ups, but also make it possible to prove problems thatwere out of reach when using so-called basic heuristics. Moreover, a combinationof these two heuristics can further increase performance.We compare our results with the results the creators of Otter obtained withthis renowned theorem prover and this way substantiate our achievements.

In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev class \(W^r_2\) is studied. The exact order of information complexity is derived. The lower bound is proved using a Gelfand number technique. The upper bound is shown by providing a concrete algorithm of optimal order, based on a specific hyperbolic cross approximation of the kernel function. Numerical experiments are included, comparing the optimal algorithm with the standard Galerkin method.

Experience gathered from applying the software process modeling language MVP-L in software development organizations has shown the need for graphical representations of process models. Project members (i.e„ non MVP-L specialists) review models much more easily by using graphical representations. Although several various graphical notations were developed for individual projects in which MVP-L was applied, there was previously no consistent definition of a mapping between textual MVP-L models and graphical representations. This report defines a graphical representation schema for MVP-L
descriptions and combines previous results in a unified form. A basic set of building blocks (i.e., graphical symbols and text fragments) is defined, but because we must first gain experience with the new symbols, only rudimentary guidelines are given for composing basic
symbols into a graphical representation of a model.

Intellectual control over software development projects requires the existence of an integrated set of explicit models of the products to be developed, the processes used to develop them, the resources needed, and the productivity and quality aspects involved. In recent years the development of languages, methods and tools for modeling software processes, analyzing and enacting them has become a major emphasis of software engineering research. The majority of current process research concentrates on prescriptive modeling of small, completely formalizable processes and their execution entirely on computers. This research direction has produced process modeling languages suitable for machine rather than human consumption. The MVP project, launched at the University of Maryland and continued at Universität Kaiserslautern, emphasizes building descriptive models of large, real-world processes and their use by humans and computers for the purpose of understanding, analyzing, guiding and improving software development projects. The language MVP-L has been developed with these purposes in mind. In this paper, we
motivate the need for MVP-L, introduce the prototype language, and demonstrate its uses. We assume that further improvements to our language will be triggered by lessons learned from applications and experiments.

Optimal degree reductions, i.e. best approximations of \(n\)-th degree Bezier curves
by Bezier curves of degree \(n\) - 1, with respect to different norms are studied. It
is shown that for any \(L_p\)-norm the euclidean degree reduction where the norm is applied to the euclidean distance function of two curves is identical to componentwise degree reduction. The Bezier points of the degree reductions are found to lie on parallel lines through the Bezier points of any Taylor expansion of degree \(n\) - 1 of the original curve. This geometric situation is shown to hold also in the case of constrained degree reduction. The Bezier points of the degree reduction are explicitly given in the unconstrained case for \(p\) = 1 and \(p\) = 2 and in the constrained case for \(p\) = 2.

The local solution problem of multivariate Fredholm integral equations is studied. Recent research proved that for several function classes the complexity of this problem is closely related to the Gelfand numbers of some characterizing operators. The generalization of this approach to the situation of arbitrary Banach spaces is the subject of the present paper.
Furthermore, an iterative algorithm is described which - under some additional conditions - realizes the optimal error rate. The way these general theorems work is demonstrated by applying them to integral equations in a Sobolev space of periodic functions with dominating mixed derivative of various order.

This paper introduces a new high Level programming language for a novel
class of computational devices namely data-procedural machines. These machines are by up to several orders of magnitude more efficient than the von Neumann paradigm of computers and are as flexible and as universal as computers. Their efficiency and flexibility is achieved by using field-programmable logic as the essential technology platform. The paper briefly summarizes and illustrates the essential new features of this language by means of two example programs.

A new variance reduction technique for the Monte Carlo solution of integral
equations is introduced. It is based on separation of the main part. A neighboring equation with exactly known solution is constructed by the help of a deterministic Galerkin scheme. The variance of the method is analyzed, and an application to the radiosity equation of computer graphics, together with numerical test results is given.

In this paper an analytic hidden surface removal algorithm is presented which uses a combination
of 2D and 3D BSP trees without involving point sampling or scan conversion. Errors like aliasing
which result from sampling do not occur while using this technique. An application of this
algorithm is outlined which computes the energy locally reflected from a surface having an
arbitrary BRDF. A simplification for diffuse reflectors is described, which has been implemented
to compute analytic form factors from diffuse light sources to differential receivers as they are needed for shading and radiosity algorithms.

The CAD/CAM-based design of free-form surfaces is the beginning of a chain of operations, which ends with the numerically controlled (NC-) production of the designed object. During this process the shape control is an important step to amount efficiency. Several surface interrogation methods already exist to analyze curvature and continuity behaviour of the shape. This paper deals with a new aspect of shape control: the stability of surfaces with respect to infnitesimal bendings. Each inEnitesimal bending of a surface determines a so called instability surface, which is used for the stability investigations. The kinematic meaning of this instability surface will be discussed and we present algorithms to calculate it.

Computer processing of free form surfaces forms the basis of a closed construction process starting with surface design and up to NC-production.
Numerical simulation and visualization allow quality analysis before manufacture. A new aspect in surface analysis is described, the stability
of surfaces versus infinitesimal bendings. The stability concept is derived
from the kinetic meaning of a special vector field which is given by the deformation. Algorithms to calculate this vector field together with an appropriate visualization method give a tool able to analyze surface stability.

The \(L_2\)-discrepancy is a quantitative measure of precision for multivariate quadrature rules. It can be computed explicitly. Previously known algorithms needed \(O(m^2\)) operations, where \(m\) is the number of nodes. In this paper we present algorithms which require
\(O(m(log m)^d)\) operations.