Kaiserslautern - Fachbereich Informatik
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Faculty / Organisational entity
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.
Orderings on polynomial interpretations of operators represent a powerful technique for proving thetermination of rewriting systems. One of the main problems of polynomial orderings concerns thechoice of the right interpretation for a given rewriting system. It is very difficult to develop techniquesfor solving this problem. Here, we present three new heuristic approaches: (i) guidelines for dealingwith special classes of rewriting systems, (ii) an algorithm for choosing appropriate special polynomialsas well as (iii) an extension of the original polynomial ordering which supports the generation ofsuitable interpretations. All these heuristics will be applied to examples in order to illustrate theirpractical relevance.
Planar force or pressure is a fundamental physical aspect during any people-vs-people and people-vs-environment activities and interactions. It is as significant as the more established linear and angular acceleration (usually acquired by inertial measurement units). There have been several studies involving planar pressure in the discipline of activity recognition, as reviewed in the first chapter. These studies have shown that planar pressure is a promising sensing modality for activity recognition. However, they still take a niche part in the entire discipline, using ad hoc systems and data analysis methods. Mostly these studies were not followed by further elaborative works. The situation calls for a general framework that can help push planar pressure sensing into the mainstream.
This dissertation systematically investigates using planar pressure distribution sensing technology for ubiquitous and wearable activity recognition purposes. We propose a generic Textile Pressure Mapping (TPM) Framework, which encapsulates (1) design knowledge and guidelines, (2) a multi-layered tool including hardware, software and algorithms, and (3) an ensemble of empirical study examples. Through validation with various empirical studies, the unified TPM framework covers the full scope of application recognition, including the ambient, object, and wearable subspaces.
The hardware part constructs a general architecture and implementations in the large-scale and mobile directions separately. The software toolkit consists of four heterogeneous tiers: driver, data processing, machine learning, visualization/feedback. The algorithm chapter describes generic data processing techniques and a unified TPM feature set. The TPM framework offers a universal solution for other researchers and developers to evaluate TPM sensing modality in their application scenarios.
The significant findings from the empirical studies have shown that TPM is a versatile sensing modality. Specifically, in the ambient subspace, a sports mat or carpet with TPM sensors embedded underneath can distinguish different sports activities or different people's gait based on the dynamic change of body-print; a pressure sensitive tablecloth can detect various dining actions by the force propagated from the cutlery through the plates to the tabletop. In the object subspace, swirl office chairs with TPM sensors under the cover can be used to detect the seater's real-time posture; TPM can be used to detect emotion-related touch interactions for smart objects, toys or robots. In the wearable subspace, TPM sensors can be used to perform pressure-based mechanomyography to detect muscle and body movement; it can also be tailored to cover the surface of a soccer shoe to distinguish different kicking angles and intensities.
All the empirical evaluations have resulted in accuracies well-above the chance level of the corresponding number of classes, e.g., the `swirl chair' study has classification accuracy of 79.5% out of 10 posture classes and in the `soccer shoe' study the accuracy is 98.8% among 17 combinations of angle and intensity.
The Analytic Blossom
(2001)
Blossoming is a powerful tool for studying and computing with Bézier and B-spline curves and surfaces - that is, for the investigation and analysis of polynomials and piecewise polynomials in geometric modeling. In this paper, we define a notion of the blossom for Poisson curves. Poisson curves are to analytic functions what Bézier curves are to polynomials - a representation adapted to geometric design. As in the polynomial setting, the blossom provides a simple, powerful, elegant and computationally meaningful way to analyze Poisson curves. Here, we
define the analytic blossom and interpret all the known algorithms for Poisson curves - subdivision, trimming, evaluation of the function and its derivatives, and conversion between the Taylor and the Poisson basis - in terms of this analytic blossom.
In this report we present a case study of employing goal-oriented heuristics whenproving equational theorems with the (unfailing) Knut-Bendix completion proce-dure. The theorems are taken from the domain of lattice ordered groups. It will bedemonstrated that goal-oriented (heuristic) criteria for selecting the next critical paircan in many cases significantly reduce the search effort and hence increase per-formance of the proving system considerably. The heuristic, goalADoriented criteriaare on the one hand based on so-called "measures" measuring occurrences andnesting of function symbols, and on the other hand based on matching subterms.We also deal with the property of goal-oriented heuristics to be particularly helpfulin certain stages of a proof. This fact can be addressed by using them in a frame-work for distributed (equational) theorem proving, namely the "teamwork-method".
We describe a platform for the portable and secure execution of mobile agents writtenin various interpreted languages on top of a common run-time core. Agents may migrate at anypoint in their execution, fully preserving their state, and may exchange messages with otheragents. One system may contain many virtual places, each establishing a domain of logicallyrelated services under a common security policy governing all agents at this place. Agents areequipped with allowances limiting their resource accesses, both globally per agent lifetime andlocally per place. We discuss aspects of this architecture and report about ongoing work.
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.
Virtual Reality (VR) is to be seen as the superset of simulation and animation. Visualization is done by rendering. The fundamental model of VR accounts for all phenomenons to be modelled with help of a computer. Examples range from simple dragging actions with a mouse device to the complex simulation of physically based animation.