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In this report we give an overview of the development of our new Waldmeisterprover for equational theories. We elaborate a systematic stepwise design process, startingwith the inference system for unfailing Knuth - Bendix completion and ending up with animplementation which avoids the main diseases today's provers suffer from: overindulgencein time and space.Our design process is based on a logical three - level system model consisting of basicoperations for inference step execution, aggregated inference machine, and overall controlstrategy. Careful analysis of the inference system for unfailing completion has revealed thecrucial points responsible for time and space consumption. For the low level of our model,we introduce specialized data structures and algorithms speeding up the running system andcutting it down in size - both by one order of magnitude compared with standard techniques.Flexible control of the mid - level aggregation inside the resulting prover is made possible by acorresponding set of parameters. Experimental analysis shows that this flexibility is a pointof high importance. We go on with some implementation guidelines we have found valuablein the field of deduction.The resulting new prover shows that our design approach is promising. We compare oursystem's throughput with that of an established system and finally demonstrate how twovery hard problems could be solved by Waldmeister.

Mit der schnellen Verbreitung der CAx-Techniken in der deutschen Automobilindustrie wächst die Notwendigkeit einer besseren Integration der CAx-Systeme in die Prozeßketten und der Beherrschung der Produktinformationsflüsse. Aufgrund dieser Tatsachen ist in den letzten Jah-ren ein Wandel der CAx-Systemarchitekturen von geschloßenen, monolithischen zu offen inte-grierten Systemen erkennbar. Im folgenden wird dieser Prozeß sowie dessen Implikationen auf die Anwendung und auf die Systemhersteller analysiert. Ausgehend von der Initiative der deutschen Automobilindustrie wurde das Projekt ANICA (Analysis of Interfaces of various CAD/CAM-Systems) gestartet. In diesem Projekt werden die Schnittstellen zu den Systemkernen einiger CAx-Hersteller untersucht und ein Konzept für kooperierende CAx-Systeme in der Automobilindustrie wird entwickelt.

Toying with Jordan matrices
(1996)

We present first steps towards fully automated deduction that merely requiresthe user to submit proof problems and pick up results. Essentially, this necessi-tates the automation of the crucial step in the use of a deduction system, namelychoosing and configuring an appropriate search-guiding heuristic. Furthermore,we motivate why learning capabilities are pivotal for satisfactory performance.The infrastructure for automating both the selection of a heuristic and integra-tion of learning are provided in form of an environment embedding the "core"deduction system.We have conducted a case study in connection with a deduction system basedon condensed detachment. Our experiments with a fully automated deductionsystem 'AutoCoDe' have produced remarkable results. We substantiate Au-toCoDe's encouraging achievements with a comparison with the renowned the-orem prover Otter. AutoCoDe outperforms Otter even when assuming veryfavorable conditions for Otter.

Abstract: We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body centered cubic solid on solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperature K_R = 0.40754(5) is almost by two orders of magnitude more accurate than the estimate of Mon, Landau and Stauffer [9].

Load balancing is one of the central problems that have to be solved in parallel computation. Here, the problem of distributed, dynamic load balancing for massive parallelism is addressed. A new local method, which realizes a physical analogy to equilibrating liquids in multi-dimensional tori or hypercubes, is presented. It is especially suited for communication mechanisms with low set-up to transfer ratio occurring in tightly-coupled or SIMD systems. By successive shifting single load elements to the direct neighbors, the load is automatically transferred to lightly loaded processors. Compared to former methods, the proposed Liquid model has two main advantages. First, the task of load sharing is combined with the task of load balancing, where the former has priority. This property is valuable in many applications and important for highly dynamic load distribution. Second, the Liquid model has high efficiency. Asymptotically, it needs O(D . K . Ldiff ) load transfers to reach the balanced state in a D-dimensional torus with K processors per dimension and a maximum initial load difference of Ldiff . The Liquid model clearly outperforms an earlier load balancing approach, the nearest-neighbor-averaging. Besides a survey of related research, analytical results within a formal framework are derived. These results are validated by worst-case simulations in one-and two-dimensional tori with up to two thousand processors.

The calculation of form factors is an important problem in computing the global illumination in the radiosity setting. Closed form solutions often are only available for objects without obstruction and are very hard to calculate. Using Monte Carlo integration and ray tracing provides a fast and elegant tool for the estimation of the form factors. In this paper we show, that using deterministic low discrepancy sample points is superior to random sampling, resulting in an acceleration of more than half an order of magnitude.

This document offers a concise introduction to the Goal Question Metric Paradigm (GQM Paradigm), and surveys research on applying and extending the GQM Paradigm. We describe the GQM Paradigm in terms of its basic principles, techniques for structuring GQM-related documents, and methods for performing tasks of planning and implementing a measurement program based on GQM. We also survey prototype software tools that support applying the GQM Paradigm in various ways. An annotated bibliography lists sources that document experience gained while using the GQM Paradigm and offer in-depth information about the GQM Paradigm.

Tangent measure distributions were introduced by Bandt and Graf as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by contractive mappings, which are not similitudes. We show that the tangent measure distributions of these sets equipped with either Hausdorff or Gibbs measure are unique almost everywhere and give an explicit formula describing them as probability distributions on the set of limit models of Bedford and Fisher.

Suppression of the magnetocrystalline bulk anisotropy in thin epitaxial Co(110) films on Cu(110)
(1996)

We report on an unexpected suppression of the magnetocrystalline anisotropy contribution in epitaxial fcc Co(110) films on Cu(110) below a thickness of dc=(50 +/- 10) Å. For film thicknesses larger than dc the measured anisotropy value agrees with published data. Measurements on films with reduced strain indicate a large strain dependence of dc . A model calculation based on a crystal-field formalism and discussed within the context of band theory, which explicitly takes tetragonal misfit strains into account, reproduces the experimen-tally observed anomalies. Our results indicate that the usually applied phenomenological description of anisotropies, assuming additive free energy terms for each anisotropy contribution, fails in this case.

This paper investigates the convergence of the Lanczos method for computing the smallest eigenpair of a selfadjoint elliptic differential operator via inverse iteration (without shifts).
Superlinear convergence rates are established, and their sharpness is investigated for a simple model problem. These results are illustrated numerically for a more difficult problem.

Structure and Construction of Instanton Bundles on P3

The magnetic anisotropy of Co/Cu~001! films has been investigated by the magneto-optical Kerr effect, both in the pseudomorphic growth regime and above the critical thickness where strain relaxation sets in. A clear correlation between the onset of strain relaxation as measured by means of reflection high-energy electron diffraction and changes of the magnetic anisotropy has been found.

Some formulae, containing logarithmic derivatives of (smooth) measures on infinitedimensional spaces, arise in quite different situations. In particular, logarithmic derivatives of a measure are inserted in the Schr"odinger equastion in the space consisting of functions that are square integrable with respect to this measure, what allows us to describe very simply a procedure of (canonical) quantization of infinite-dimensional Hamiltonian systems with the linear phase space. Further, the problem of reconstructing of a measure by its logarithmic derivative (that was posed in [1] independently of any applications) can be equivalent either to the problem of finding the "ground state" (considered as some measure) for infinite-dimensional Schr"odinger equation, or to the problem of finding an invariant measure for a stochastic differential equation (that is a central question of so-called stochastic quantization), or to the problem of recenstruc ting "Gibbsian measure by its specification" (i.e. by a collection of finite-dimensional conditional distributions). Logarithmic derivatives of some measure appear in Cameron-Martin-Girsanov-Maruyama formulae and in its generalizations related to arbitrary smooth measures; they allow also to connect these formulae and the Feynman-Kac formulae. This note discusses all these topics. Of course due to its shortness the presentation is formal in main, and precise analitical assumptions are usually absent. Actually only a list of formulae with small comments is given. Let us mention also that we do not consider at all so-called Dirichlet forms to which a great deal of literature is devoted (cf. [3] and references therein to the works of S. Alberion and others).

The paper presents some new estimates on the gain term of the Boltzmann collision operator. For Maxwellian molecules, it is shown that the L -norm of the gain term can be bounded in terms of the L1 and L -norm of the density function f. In the case of more general collision kernels, like the hard-sphere interaction potential, the gain term is estimated pointwise by the L -norm of the density function and the loss term of the Boltzmann collision operator.

The purpose of this paper is to present the state of the art in singular optimal control. If the Hamiltonian in an interval \([t_1,t_2]\) is independent of the control we call the control in this interval singular. Singular optimal controls appear in many applications so that research has been motivated since the 1950s. Often optimal controls consist of nonsingular and singular parts where the junctions between these parts are mostly very difficult to find. One section of this work shows the actual knowledge about the location of the junctions and the behaviour of the control at the junctions. The definition and the properties of the orders (problem order and arc order), which are important in this context, are given, too. Another chapter considers multidimensional controls and how they can be treated. An alternate definition of the orders in the multidimensional case is proposed and a counterexample, which confirms a remark given in the 1960s, is given. A voluminous list of optimality conditions, which can be found in several publications, is added. A strategy for solving optimal control problems numerically is given, and the existing algorithms are compared with each other. Finally conclusions and an outlook on the future research is given.

Significance of zero modes in path-integral quantization of solitonic theories with BRST invariance
(1996)

The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1 + 2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to -the one-loop approximation.

For the case of the single-O(N)-vector linear sigma models the critical behaviour following from any A_k singularity in the action is worked out in the double scaling limit N->infinity, f_r -> f_r^c, 2 <= r <= k. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for all A_k and spacetime dimensions 0 <= D <= 4. There appear exceptional spacetime dimensions where the degree k of the singularity A_k is more strongly constrained than by the renormalizability requirement.

This article will discuss a qualitative, topological and robust world-modelling technique with special regard to navigation-tasks for mobile robots operating in unknownenvironments. As a central aspect, the reliability regarding error-tolerance and stability will be emphasized. Benefits and problems involved in exploration, as well as in navigation tasks, are discussed. The proposed method demands very low constraints for the kind and quality of the employed sensors as well as for the kinematic precision of 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

Es wird das Lernen uniform rekursiv aufzählbarer Sprachfamilien anhand guter Beispiele untersucht und Unterschiede und Gemeinsamkeiten zum Lernen von rekursiven Sprachfamilien und rekursiven Funktionen aufgezeigt. Dem verwendeten Modell liegt das Lernen von Schülern mit einem Lehrer zugrunde. Es werden verschiedene Varianten vorgestellt, verglichen und teilweise auch charakterisiert, und versucht, mit Beispielen und anderen typischen Eigenschaften ein Gefühl für die Leistungsfähigkeit zu vermitteln. Unter anderem wird gezeigt, dass es nicht immer "universelle" gute Beispiele gibt, mit denen eine Sprachklasse in allen Situationen erklärt werden kann.

This paper develops truncated Newton methods as an appropriate tool for nonlinear inverse problems which are ill-posed in the sense of Hadamard. In each Newton step an approximate solution for the linearized problem is computed with the conjugate gradient method as an inner iteration. The conjugate gradient iteration is terminated when the residual has been reduced to a prescribed percentage. Under certain assumptions on the nonlinear operator it is shown that the algorithm converges and is stable if the discrepancy principle is used to terminate the outer iteration.
These assumptions are fulfilled , e.g., for the inverse problem of identifying the diffusion coefficient in a parabolic differential equation from distributed data.

Ein umfangreiches Gebiet der Künstlichen Intelligenz beschäftigt sich mit dem Bereich Planung. Im wesentlichen gibt es zwei Planungsansätze, zum einen nicht-hierarchische und zum anderen hierarchische arbeitende Verfahren. Als Beispiel für einen nicht-hierarchischen Ansatz kann SNLP1 genannt werden. Die nachfolgende Ausarbeitung ist auf dem zweiten Gebiet, der hierarchischen Planung, angesiedelt: Der Planungsassistent CAPlan2, der eigentlich auf dem nicht-hierarchischen Planungsansatz SNLP beruht, soll um die Möglichkeiten der hierarchischen Planung erweitert werden.

We have presented a novel approach to parallel motion planning for robot manipulators in 3D workspaces. The approach is based on arandomized parallel search algorithm and focuses on solving the path planning problem for industrial robot arms working in a reasonably cluttered workspace. The path planning system works in the discretized con guration space, which needs not to be represented explicitly. The parallel search is conducted by a number of rule-based sequential search processes, which work to find a path connecting the initial con guration to the goal via a number of randomly generated subgoal con gurations. Since the planning performs only on-line collision tests with proper proximity information without using pre-computed information, the approach is suitable for planning problems with multirobot or dynamic environments. The implementation has been carried outontheparallel virtual machine (PVM) of a cluster of SUN4 workstations and SGI machines. The experimental results have shown that the approach works well for a 6-dof robot arm in a reasonably cluttered environment, and that parallel computation increases the e ciency of motion planning signi cantly.

Quasi-Monte Carlo Radiosity
(1996)

The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating
solutions to this transport equation. For the case of the radiosity equation, we present the deterministic method of quasi-rondom walks. This method very efficiently uses low discrepancy sequences for integrating the Neumann series and consistently outperforms stochastic techniques. The method of quasi-random walks also is applicable to transport problems in settings other
than computer graphics.

The constraint structure of the induced 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge does not exist, whereas there is the possibility to choose the so-called "quasi-light-cone" gauge, in which besides the area-preserving diffeomorphism invariance, the reduced Lagrangian also possesses the SL(2,R) residual symmetry. This observation indicates that the claimed correspondence between the SL(2,R) residual symmetry and the area-preserving diffeomorphism invariance in both regularisation approaches does not hold. The string-like approach is then applied to quantise this model, but a fictitious non-zero central charge in the Virasoro algebra appears. When a set of gauge-independent SL(2,R) current-like fields is introduced instead of the string-like variables, a consistent quantum theory is obtained, which means that the area-preserving diffeomorphism invariance can be maintained at the quantum level.

Problemspezifikation für die Arbeitsplanerstellung rotationssymmetrischer Drehteile mit AutoCAD
(1996)

Um den Anforderungen am industriellen Markt gerecht werden zu können, sind Unternehmer gezwungen, immer komplexere, speziell auf den Kunden abgestimmte Produkte möglichst schnell in kleinen Losgrössen herzustellen. Dabei umfasst die Herstellung eines neuen Produkts eine Vielzahl von Arbeitsschritten. Um den Marktanforderungen zu genügen wird bereits heute ein grosser Teil dieser Arbeitsvorgänge computerunterstützt durchgeführt.

A polynomial function \(f : L \to L\) of a lattice \(\mathcal{L}\) = \((L; \land, \lor)\) is generated by the identity function id \(id(x)=x\) and the constant functions \(c_a (x) = a\) (for every \(x \in L\)), \(a \in L\) by applying the operations \(\land, \lor\) finitely often. Every polynomial function in one or also in several variables is a monotone function of \(\mathcal{L}\).
If every monotone function of \(\mathcal{L}\)is a polynomial function then \(\mathcal{L}\) is called orderpolynomially complete. In this paper we give a new characterization of finite order-polynomially lattices. We consider doubly irreducible monotone functions and point out their relation to tolerances, especially to central relations. We introduce chain-compatible lattices
and show that they have a non-trivial congruence if they contain a finite interval and an infinite chain. The consequences are two new results. A modular lattice \(\mathcal{L}\) with a finite interval is order-polynomially complete if and only if \(\mathcal{L}\) is finite projective geometry. If \(\mathcal{L}\) is simple modular lattice of infinite length then every nontrivial interval is of infinite length and has the same cardinality as any other nontrivial interval of \(\mathcal{L}\). In the last sections we show the descriptive power of polynomial functions of
lattices and present several applications in geometry.

Planning for manufacturing workpieces is a complex task that requires the interaction of a domain-specific reasoner and a generic planning mechanism. In this paper we present an architecture for organizing the case base that is based on the information provided by a generic problem solver. A retrieval procedure is then presented that uses the information provided by the domain-specific reasoner in order to improve the accuracy of the cases retrieved. However, it is not realistic to suppose that the case retrieved will entirely fit into the new problem. We present a replay procedure to obtain a partial solution that replays not only the valid decisions taken for solving the case, but also justifications of rejected decisions made during the problem solving process. As a result, those completion alternatives of the partial solution are discarded that are already known to be invalid from the case.

The paper presents a novel approach to parallel motion planning for robot manipulators in 3D workspaces. The approach is based on a randomized parallel search algorithm and focuses on solving the path planning problem for industrial robot arms working in a reasonably cluttered workspace. The path planning system works in the discretized configuration space which needs not to be represented explicitly. The parallel search is conducted by a number of rule-based sequential search processes, which work to nd a path connecting the initial configuration to the goal via a number of randomly generated subgoal configurations. Since the planning performs only on-line collision tests with proper proximity information without using pre-computed information, the approach is suitable for planning problems with multirobot or dynamic environments. The implementation has been carried out on the parallel virtual machine (PVM) of a cluster of SUN4 workstations and SGI machines. The experimental results have shown that the approach works well for a 6-dof robot arm in a reasonably cluttered environment, and that parallel computation increases the efficiency of motion planning significantly.

Skelettbasierte implizite Flächen haben aufgrund ihrer Fähigkeit, durch automatisches Verschmelzen aus wenigen, einfachen Primitiven komplexe Strukturen zu formen, für Modellierung, Visualisierung und Animation zunehmend an Bedeutung gewonnen. Eine wesentliche Schwierigkeit beim Einsatz impliziter Flächen ist nach wie vor eine effiziente Visualisierung der resultierenden Objekte. In der vorliegenden
Arbeit werden die grundlegenden Ideen einer Methode zur partikelgestützten Triangulierung skelettbasierter impliziter Flächen beschrieben, die die Vorteile einer partikelgestützten Abtastung
impliziter Flächen mit der polygonalen Darstellung durch Dreiecke kombiniert. Der Algorithmus ist in der Lage, effizient auf dynamische Veränderungen der Gestalt sowie das Auseinanderreißen nicht allzu
komplexer implizit gegebener Objekte zu reagieren. Zusätzlich besteht die Möglichkeit, die Triangulierung krümmungsadaptiv zu gestalten, um bei gleichbleibender Darstellungsqualität eine Reduktion der Dreiecksanzahl zu erreichen.

Paris (Plan Abstraction and Refinement in an Integrated System) [4, 2] is a domain independent case-based planning system which allows the flexible reuse of planning cases by abstraction and refinement. This approach is mainly inspired by the observation that reuse of plans must not be restricted to a single description level. In domains with a high variation in the problems, the reuse of past solutions must be achieved at various levels of abstraction.

We present a novel approach to classification, based on a tight coupling of instancebased learning and a genetic algorithm. In contrast to the usual instance-based learning setting, we do not rely on (parts of) the given training set as the basis of a nearestneighbor classifier, but we try to employ artificially generated instances as concept prototypes. The extremely hard problem of finding an appropriate set of concept prototypes is tackled by a genetic search procedure with the classification accuracy on the given training set as evaluation criterion for the genetic fitness measure. Experiments with artificial datasets show that - due to the ability to find concise and accurate concept descriptions that contain few, but typical instances - this classification approach is considerably robust against noise, untypical training instances and irrelevant attributes. These favorable (theoretical) properties are corroborated using a number of hard real-world classification problems.

This paper considers a transmission boundary-value problem for the time-harmonic Maxwell equations neglecting displacement currents which is frequently used for the numerical computation of eddy-currents. Across material boundaries the tangential components of the magnetic field H and the normal component of the magnetization müH are assumed to be continuous. this problem admits a hyperplane of solutions if the domains under consideration are multiply connected. Using integral equation methods and singular perturbation theory it is shown that this hyperplane contains a unique point which is the limit of the classical electromagnetic transmission boundary-value problem for vanishing displacement currents. Considering the convergence proof, a simple contructive criterion how to select this solution is immediately derived.

The paper deals with parallel-machine and open-shop scheduling problems with preemptions and arbitrary nondecreasing objective function. An approach to describe
the solution region for these problems and to reduce them to minimization problems on polytopes is proposed. Properties of the solution regions for certain problems are investigated. lt is proved that open-shop problems with unit processing times are equivalent to certain parallel-machine problems, where preemption is allowed at arbitrary time. A polynomial algorithm is presented transforming a schedule of one type into a schedule of the other type.

This paper addresses the role of abstraction in case-based reasoning. We develop a general framework for reusing cases at several levels of abstraction, which is particularly suited for describing and analyzing existing and designing new approaches of this kind. We show that in synthetic tasks (e.g. configuration, design, and planning), abstraction can be successfully used to improve the efficiency of similarity assessment, retrieval, and adaptation. Furthermore, a case-based planning system, called Paris, is described and analyzed in detail using this framework. An empirical study done with Paris demonstrates significant advantages concerning retrieval and adaptation efficiency as well as flexibility of adaptation. Finally, we show how other approaches from the literature can be classified according to the developed framework.

Let \(a_1,\dots,a_m\) be independent random points in \(\mathbb{R}^n\) that are independent and identically distributed spherically symmetrical in \(\mathbb{R}^n\). Moreover, let \(X\) be the random polytope generated as the convex hull of \(a_1,\dots,a_m\) and let \(L_k\) be an arbitrary \(k\)-dimensional
subspace of \(\mathbb{R}^n\) with \(2\le k\le n-1\). Let \(X_k\) be the orthogonal projection image of \(X\) in \(L_k\). We call those vertices of \(X\), whose projection images in \(L_k\) are vertices of \(X_k\)as well shadow vertices of \(X\) with respect to the subspace \(L_k\) . We derive a distribution independent sharp upper bound for the expected number of shadow vertices of \(X\) in \(L_k\).

On derived varieties
(1996)

Derived varieties play an essential role in the theory of hyperidentities. In [11] we have shown that derivation diagrams are a useful tool in the analysis of derived algebras and varieties. In this paper this tool is developed further in order to use it for algebraic constructions of derived algebras. Especially the operator \(S\) of subalgebras, \(H\) of homomorphic irnages and \(P\) of direct products are studied. Derived groupoids from the groupoid \(N or (x,y)\) = \(x'\wedge y'\) and from abelian groups are considered. The latter class serves as an example for fluid algebras and varieties. A fluid variety \(V\) has no derived variety as a subvariety and is introduced as a counterpart for solid varieties. Finally we use a property of the commutator of derived algebras in order to show that solvability and nilpotency are preserved under derivation.

A convergence rate is established for nonstationary iterated Tikhonov regularization, applied to ill-posed problems involving closed, densely defined linear operators, under general conditions on the iteration parameters. lt is also shown that an order-optimal accuracy is attained when a certain a posteriori stopping rule is used to determine the iteration number.

Die Theorie der mehrdimensionalen Systeme ist ein relativ junges Forschungsgebiet innerhalb der Systemtheorie, erste Arbeiten stammen aus den 70er Jahren. Hauptmotiv für das Studium multidimensionaler Systeme war die Notwendigkeit einer Erweiterung der Theorie der digitalen Filter, die in der klassischen, eindimensionalen Signalverarbeitung (zeitabhängige Signale) Anwendung finden, auf den Bereich der Bildverarbeitung, also auf zweidimensionale Signale.; Die Vorlesung beschäftigt sich daher in ihrem ersten Teil mit skalaren zweidimensionalen Systemen und beschränkt sich im wesentlichen auf den linearen Fall. Untersucht werden zweidimensionale Filter, ihre wichtigsten Eigenschaften, Kausalität und Stabilität, sowie ihre Zustandsraum- realisierungen, etwa die Modelle von Roesser und Fornasini-Marchesini. Parallelen und Unterschiede zur eindimensionalen Systemtheorie werden betont.; Im zweiten Teil der Vorlesung werden allgemeine höherdimensionale und multivariable Systeme behandelt. Für diese Systeme erweist sich der von Jan Willems begründete Zugang zur Systemtheorie, der sogenannte behavioral approach, als zweckmäßig. Grundlegende Ideen dieses Ansatzes sowie eine der wichtigsten Methoden zum Rechnen mit Polynomen in mehreren Variablen, die Theorie der Gröbnerbasen, werden vorgestellt.