004 Datenverarbeitung; Informatik
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This document presents an axiom selection technique for classic first order theorem proving based on the relevance of axioms for the proof of a conjecture. It is based on unifiability of predicates and does not need statistical information like symbol frequency. The scope of the technique is the reduction of the set of axioms and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the axiom set, it can be used as a preprocessor for automated theorem proving. This technical report describes the conception, implementation and evaluation of ARDE. The selection method, which is based on a breadth-first graph search by unifiability of predicates, is a weakened form of the connection calculus and uses specialised variants or unifiability to speed up the selection. The implementation of the concept is evaluated with comparison to the results of the world championship of theorem provers of the year 2012 (CASC J6). It is shown that both the theorem prover leanCoP which uses the connection calculus and E which uses equality reasoning, can benefit from the selection approach. Also, the evaluation shows that the concept is applyable for theorem proving problems with thousands of formulae and that the selection is independent from the calculus used by the theorem prover.
Die stetige Weiterentwicklung von VR-Systemen bietet neue Möglichkeiten der Interaktion mit virtuellen Objekten im dreidimensionalen Raum, stellt Entwickelnde von VRAnwendungen aber auch vor neue Herausforderungen. Selektions- und Manipulationstechniken müssen unter Berücksichtigung des Anwendungsszenarios, der Zielgruppe und der zur Verfügung stehenden Ein- und Ausgabegeräte ausgewählt werden. Diese Arbeit leistet einen Beitrag dazu, die Auswahl von passenden Interaktionstechniken zu unterstützen. Hierfür wurde eine repräsentative Menge von Selektions- und Manipulationstechniken untersucht und, unter Berücksichtigung existierender Klassifikationssysteme, eine Taxonomie entwickelt, die die Analyse der Techniken hinsichtlich interaktionsrelevanter Eigenschaften ermöglicht. Auf Basis dieser Taxonomie wurden Techniken ausgewählt, die in einer explorativen Studie verglichen wurden, um Rückschlüsse auf die Dimensionen der Taxonomie zu ziehen und neue Indizien für Vor- und Nachteile der Techniken in spezifischen Anwendungsszenarien zu generieren. Die Ergebnisse der Arbeit münden in eine Webanwendung, die Entwickelnde von VR-Anwendungen gezielt dabei unterstützt, passende Selektions- und Manipulationstechniken für ein Anwendungsszenario auszuwählen, indem Techniken auf Basis der Taxonomie gefiltert und unter Verwendung der Resultate aus der Studie sortiert werden können.
Aufzählen von DNA-Codes
(2006)
In dieser Arbeit wird ein Modell zum Aufzählen von DNA-Codes entwickelt. Indem eine Ordnung auf der Menge aller DNA-Codewörter eingeführt und auf die Menge aller Codes erweitert wird, erlaubt das Modell das Auffinden von DNA-Codes mit bestimmten Eigenschaften, wie Überlappungsfreiheit, Konformität, Kommafreiheit, Stickyfreiheit, Überhangfreiheit, Teilwortkonformität und anderer bezüglich einer gegebenen Involution auf der Menge der Codewörter. Ein auf Grundlage des geschaffenen Modells entstandenes Werkzeug erlaubt das Suchen von Codes mit beliebigen Kombinationen von Codeeigenschaften. Ein weiterer wesentlicher Bestandteil dieser Arbeit ist die Untersuchung der Optimalität von DNA-Codes bezüglich ihrer Informationsrate sowie das Finden solider DNA-Codes.
Die gelungene Durchführung einer Vorlesung „Informatik I – Einführung in die Programmierung“ ist schwierig, trotz einer Vielfalt existierender Materialien und erprobter didaktischer Methoden. Gerade aufgrund dieser vielfältigen Auswahl hat sich bisher noch kein robustes Konzept durchgesetzt, das unabhängig von den Durchführenden eine hohe Erfolgsquote garantiert. An den Universitäten Tübingen und Freiburg wurde die Informatik I aus den gleichen Lehrmaterialien und unter ähnlichen Bedingungen durchgeführt, um das verwendete Konzept auf Robustheit zu überprüfen. Die Grundlage der Vorlesung bildet ein systematischer Ansatz zum Erlernen des Programmierens, der von der PLTGruppe in USA entwickelt worden ist. Hinzu kommen neue Ansätze zur Betreuung, insbesondere das Betreute Programmieren, bei dem die Studierenden eine solide Basis für ihre Programmierfähigkeiten entwickeln. Der vorliegende Bericht beschreibt hierbei gesammelte Erfahrungen, erläutert die Entwicklung der Unterrichtsmethodik und der Inhaltsauswahl im Vergleich zu vorangegangenen Vorlesungen und präsentiert Daten zum Erfolg der Vorlesung.
Most of the microelectronic circuits fabricated today are synchronous, i.e. they are driven by one or several clock signals. Synchronous circuit design faces several fundamental challenges such as high-speed clock distribution, integration of multiple cores operating at different clock rates, reduction of power consumption and dealing with voltage, temperature, manufacturing and runtime variations. Asynchronous or clockless design plays a key role in alleviating these challenges, however the design and test of asynchronous circuits is much more difficult in comparison to their synchronous counterparts. A driving force for a widespread use of asynchronous technology is the availability of mature EDA (Electronic Design Automation) tools which provide an entire automated design flow starting from an HDL (Hardware Description Language) specification yielding the final circuit layout. Even though there was much progress in developing such EDA tools for asynchronous circuit design during the last two decades, the maturity level as well as the acceptance of them is still not comparable with tools for synchronous circuit design. In particular, logic synthesis (which implies the application of Boolean minimisation techniques) for the entire system's control path can significantly improve the efficiency of the resulting asynchronous implementation, e.g. in terms of chip area and performance. However, logic synthesis, in particular for asynchronous circuits, suffers from complexity problems. Signal Transitions Graphs (STGs) are labelled Petri nets which are a widely used to specify the interface behaviour of speed independent (SI) circuits - a robust subclass of asynchronous circuits. STG decomposition is a promising approach to tackle complexity problems like state space explosion in logic synthesis of SI circuits. The (structural) decomposition of STGs is guided by a partition of the output signals and generates a usually much smaller component STG for each partition member, i.e. a component STG with a much smaller state space than the initial specification. However, decomposition can result in component STGs that in isolation have so-called irreducible CSC conflicts (i.e. these components are not SI synthesisable anymore) even if the specification has none of them. A new approach is presented to avoid such conflicts by introducing internal communication between the components. So far, STG decompositions are guided by the finest output partitions, i.e. one output per component. However, this might not yield optimal circuit implementations. Efficient heuristics are presented to determine coarser partitions leading to improved circuits in terms of chip area. For the new algorithms correctness proofs are given and their implementations are incorporated into the decomposition tool DESIJ. The presented techniques are successfully applied to some benchmarks - including 'real-life' specifications arising in the context of control resynthesis - which delivered promising results.
In this paper we describe the recent state of our research
project concerning computer science teachers’ knowledge on students’
cognition. We did a comprehensive analysis of textbooks, curricula
and other resources, which give teachers guidance to formulate assignments.
In comparison to other subjects there are only a few concepts
and strategies taught to prospective computer science teachers in university.
We summarize them and given an overview on our empirical
approach to measure this knowledge.
This thesis presents methods for automated synthesis of flexible chip multiprocessor systems from parallel programs targeted at FPGAs to exploit both task-level parallelism and architecture customization. Automated synthesis is necessitated by the complexity of the design space. A detailed description of the design space is provided in order to determine which parameters should be modeled to facilitate automated synthesis by optimizing a cost function, the emphasis being placed on inclusive modeling of parameters from application, architectural and physical subspaces, as well as their joint coverage in order to avoid pre-constraining the design space. Given a parallel program and a set of an IP library, the automated synthesis problem is to simultaneously (i) select processors (ii) map and schedule tasks to them, and (iii) select one or several networks for inter-task communications such that design constraints and optimization objectives are met. The research objective in this thesis is to find a suitable model for automated synthesis, and to evaluate methods of using the model for architectural optimizations. Our contributions are a holistic approach for the design of such systems, corresponding models to facilitate automated synthesis, evaluation of optimization methods using state of the art integer linear and answer set programming, as well as the development of synthesis heuristics to solve runtime challenges.
Projektmanagement-Kompetenzen werden von Unternehmen unterschiedlichster Branchen mit wachsender Priorität betrachtet und eingefordert. Als Beitrag zu einer kompetenzorientierten Ausbildung werden in diesem Paper interdisziplinäre Studienmodule als Bestandteil des Wirtschaftsinformatik-Studiums vorgestellt. Zielsetzung der Studienmodule ist die Befähigung der Studierenden, konkrete Projekte unter Nutzung von standardisierten Werkzeugen und Methoden nach dem IPMA-Standard planen und durchführen zu können.
Advances in biotechnologies rapidly increase the number of molecules of a cell which can be observed simultaneously. This includes expression levels of thousands or ten-thousands of genes as well as concentration levels of metabolites or proteins. Such Profile data, observed at different times or at different experimental conditions (e.g., heat or dry stress), show how the biological experiment is reflected on the molecular level. This information is helpful to understand the molecular behaviour and to identify molecules or combination of molecules that characterise specific biological condition (e.g., disease). This work shows the potentials of component extraction algorithms to identify the major factors which influenced the observed data. This can be the expected experimental factors such as the time or temperature as well as unexpected factors such as technical artefacts or even unknown biological behaviour. Extracting components means to reduce the very high-dimensional data to a small set of new variables termed components. Each component is a combination of all original variables. The classical approach for that purpose is the principal component analysis (PCA). It is shown that, in contrast to PCA which maximises the variance only, modern approaches such as independent component analysis (ICA) are more suitable for analysing molecular data. The condition of independence between components of ICA fits more naturally our assumption of individual (independent) factors which influence the data. This higher potential of ICA is demonstrated by a crossing experiment of the model plant Arabidopsis thaliana (Thale Cress). The experimental factors could be well identified and, in addition, ICA could even detect a technical artefact. However, in continuously observations such as in time experiments, the data show, in general, a nonlinear distribution. To analyse such nonlinear data, a nonlinear extension of PCA is used. This nonlinear PCA (NLPCA) is based on a neural network algorithm. The algorithm is adapted to be applicable to incomplete molecular data sets. Thus, it provides also the ability to estimate the missing data. The potential of nonlinear PCA to identify nonlinear factors is demonstrated by a cold stress experiment of Arabidopsis thaliana. The results of component analysis can be used to build a molecular network model. Since it includes functional dependencies it is termed functional network. Applied to the cold stress data, it is shown that functional networks are appropriate to visualise biological processes and thereby reveals molecular dynamics.
Zur Unterstützung von Studierenden in der Studieneingangsphase wurde an der RWTH Aachen ein neuartiger und motivierender Einstieg in den Vorkurs Informatik entwickelt und zum Wintersemester 2011/12 erprobt. Dabei wurde die grafische Programmierung mittels App Inventor eingeführt, die zur Umsetzung anwendungsbezogener Projekte genutzt wurde. In diesem Beitrag werden die Motivation für die Neugestaltung, das Konzept und die Evaluation des Testlaufs beschrieben. Diese dienen als Grundlage für eine vollständige Neukonzeption des Vorkurses für das Wintersemester 2012/2013.
Erstsemester-Studierende sind mit den Anforderungen des Lehr-/ Lernprozess einer Universität oder Fachhochschule noch nicht vertraut. Ihre Erwartungen orientieren sich vielmehr an ihrer bisherigen Lerngeschichte (Abitur, Fachabitur, o. ä.). Neben den fachlichen Anforderungen des ersten Semesters müssen die Studierenden also auch Veränderungen im Lehr-/Lernprozess erkennen und bewältigen. Es wird anhand einer Output-orientierten
informatischen Lehrveranstaltung aufgezeigt, dass sich aus deren strengen Anforderungen der Messbarkeit klare Kompetenzbeschreibungen ergeben, die besonders dem Orientierungsbedürfnis Erstsemester-Studierender entgegenkommen.
Die Studieneingangsphase stellt für Studierende eine Schlüsselphase des tertiären Ausbildungsabschnitts dar. Fachwissenschaftliches Wissen wird praxisfern vermittelt und die Studierenden können die Zusammenhänge zwischen den Themenfeldern der verschiedenen Vorlesungen nicht erkennen. Zur Verbesserung der Situation wurde ein Workshop entwickelt, der die Verbindung der Programmierung und der Datenstrukturen vertieft. Dabei wird das Spiel Go-Moku1 als Android-App von den Studierenden selbständig entwickelt. Die Kombination aus Software (Java, Android-SDK) und Hardware (Tablet-Computer) für ein kleines realistisches Softwareprojekt stellt für die Studierenden eine neue Erfahrung dar.
Modern biological analysis techniques supply scientists with various forms of data. One category of such data are the so called "expression data". These data indicate the quantities of biochemical compounds present in tissue samples. Recently, expression data can be generated at a high speed. This leads in turn to amounts of data no longer analysable by classical statistical techniques. Systems biology is the new field that focuses on the modelling of this information. At present, various methods are used for this purpose. One superordinate class of these methods is machine learning. Methods of this kind had, until recently, predominantly been used for classification and prediction tasks. This neglected a powerful secondary benefit: the ability to induce interpretable models. Obtaining such models from data has become a key issue within Systems biology. Numerous approaches have been proposed and intensively discussed. This thesis focuses on the examination and exploitation of one basic technique: decision trees. The concept of comparing sets of decision trees is developed. This method offers the possibility of identifying significant thresholds in continuous or discrete valued attributes through their corresponding set of decision trees. Finding significant thresholds in attributes is a means of identifying states in living organisms. Knowing about states is an invaluable clue to the understanding of dynamic processes in organisms. Applied to metabolite concentration data, the proposed method was able to identify states which were not found with conventional techniques for threshold extraction. A second approach exploits the structure of sets of decision trees for the discovery of combinatorial dependencies between attributes. Previous work on this issue has focused either on expensive computational methods or the interpretation of single decision trees a very limited exploitation of the data. This has led to incomplete or unstable results. That is why a new method is developed that uses sets of decision trees to overcome these limitations. Both the introduced methods are available as software tools. They can be applied consecutively or separately. That way they make up a package of analytical tools that usefully supplement existing methods. By means of these tools, the newly introduced methods were able to confirm existing knowledge and to suggest interesting and new relationships between metabolites.
This thesis addresses real-time rendering techniques for 3D information lenses based on the focus & context metaphor. It analyzes, conceives, implements, and reviews its applicability to objects and structures of virtual 3D city models. In contrast to digital terrain models, the application of focus & context visualization to virtual 3D city models is barely researched. However, the purposeful visualization of contextual data of is extreme importance for the interactive exploration and analysis of this field. Programmable hardware enables the implementation of new lens techniques, that allow the augmentation of the perceptive and cognitive quality of the visualization compared to classical perspective projections. A set of 3D information lenses is integrated into a 3D scene-graph system: • Occlusion lenses modify the appearance of virtual 3D city model objects to resolve their occlusion and consequently facilitate the navigation. • Best-view lenses display city model objects in a priority-based manner and mediate their meta information. Thus, they support exploration and navigation of virtual 3D city models. • Color and deformation lenses modify the appearance and geometry of 3D city models to facilitate their perception. The presented techniques for 3D information lenses and their application to virtual 3D city models clarify their potential for interactive visualization and form a base for further development.
The main objective of this dissertation is to analyse prerequisites, expectations, apprehensions, and attitudes of students studying computer science, who are willing to gain a bachelor degree. The research will also investigate in the students’ learning style according to the Felder-Silverman model. These investigations fall in the attempt to make an impact on reducing the “dropout”/shrinkage rate among students, and to suggest a better learning environment.
The first investigation starts with a survey that has been made at the computer science department at the University of Baghdad to investigate the attitudes of computer science students in an environment dominated by women, showing the differences in attitudes between male and female students in different study years. Students are accepted to university studies via a centrally controlled admission procedure depending mainly on their final score at school. This leads to a high percentage of students studying subjects they do not want. Our analysis shows that 75% of the female students do not regret studying computer science although it was not their first choice. And according to statistics over previous years, women manage to succeed in their study and often graduate on top of their class. We finish with a comparison of attitudes between the freshman students of two different cultures and two different university enrolment procedures (University of Baghdad, in Iraq, and the University of Potsdam, in Germany) both with opposite gender majority.
The second step of investigation took place at the department of computer science at the University of Potsdam in Germany and analyzes the learning styles of students studying the three major fields of study offered by the department (computer science, business informatics, and computer science teaching). Investigating the differences in learning styles between the students of those study fields who usually take some joint courses is important to be aware of which changes are necessary to be adopted in the teaching methods to address those different students. It was a two stage study using two questionnaires; the main one is based on the Index of Learning Styles Questionnaire of B. A. Solomon and R. M. Felder, and the second questionnaire was an investigation on the students’ attitudes towards the findings of their personal first questionnaire. Our analysis shows differences in the preferences of learning style between male and female students of the different study fields, as well as differences between students with the different specialties (computer science, business informatics, and computer science teaching).
The third investigation looks closely into the difficulties, issues, apprehensions and expectations of freshman students studying computer science. The study took place at the computer science department at the University of Potsdam with a volunteer sample of students. The goal is to determine and discuss the difficulties and issues that they are facing in their study that may lead them to think in dropping-out, changing the study field, or changing the university. The research continued with the same sample of students (with business informatics students being the majority) through more than three semesters. Difficulties and issues during the study were documented, as well as students’ attitudes, apprehensions, and expectations. Some of the professors and lecturers opinions and solutions to some students’ problems were also documented. Many participants had apprehensions and difficulties, especially towards informatics subjects. Some business informatics participants began to think of changing the university, in particular when they reached their third semester, others thought about changing their field of study. Till the end of this research, most of the participants continued in their studies (the study they have started with or the new study they have changed to) without leaving the higher education system.
Diese Arbeit enthält eine umfassende Analyse, wie der Kompetenzerwerb in einem einsemestrigen Softwarepraktikum vonstatten geht. Dabei steht neben der Frage, welche Kompetenzen besonders gut erworben wurden, der Einfluss von Vorwissen/-kompetenz im Mittelpunkt der Abhandlung. Auf dieser Basis werden einige grundlegende und konkrete Verbesserungsvorschläge erarbeitet, wie der breite Kompetenzerwerb begünstigt wird, d.h. möglichst viele Studierende sich in einem breiten Kompetenzspektrum weiterentwickeln.
In der letzten Jahren ist die Zahl der erfolgreichen Prüfungen von Studierenden im Informatikkurs des ersten Studienjahres für verschiedene Studiengänge an der Universität Óbuda stark gesunken. Dies betrifft Prüfungen in den Teilgebieten Rechnerarchitektur, Betrieb von Peripheriegeräten, Binäre Codierung und logische Operationen, Computerviren, Computernetze und das Internet, Steganographie und Kryptographie, Betriebsysteme. Mehr als der Hälfte der Studenten konnte die Prüfungen der ersten Semester nicht erfolgreich absolvieren. Die hier vorgelegte Analyse der Studienleistungen zielt darauf ab, Gründe für diese Entwicklung zu identifizieren, die Zahl der Abbrecher zu reduzieren und die Leistungen der Studenten zu verbessern. Die Analyse zeigt, dass die Studenten die erforderlichen Lehrmaterialen erst ein bis zwei Tage vor oder sogar erst am Tag der Klausuren vom Server downloaden, so dass sie nicht mehr hinreichend Zeit zum Lernen haben. Diese Tendenz zeigt sich bei allen Teilgebieten des Studiengangs. Ein Mangel an kontinuierlicher Mitarbeit scheint einer der Gründe für ein frühes Scheitern zu sein. Ferner zeigt sich die Notwendigkeit, dass bei den Lehrangeboten in Informatik auf eine kontinuierliche Kommunikation mit den Studierenden und Rückmeldung zu aktuellen Unterrichtsinhalten zu achten ist. Dies kann durch motivierende Maßnahmen zur Teilnahme an den Übungen oder durch kleine wöchentliche schriftliche Tests geschehen.
Although educational content in electronic form is increasing dramatically, its usage in an educational environment is poor, mainly due to the fact that there is too much of (unreliable) redundant, and not relevant information. Finding appropriate answers is a rather difficult task being reliant on the user filtering of the pertinent information from the noise. Turning knowledge bases like the online tele-TASK archive into useful educational resources requires identifying correct, reliable, and "machine-understandable" information, as well as developing simple but efficient search tools with the ability to reason over this information. Our vision is to create an E-Librarian Service, which is able to retrieve multimedia resources from a knowledge base in a more efficient way than by browsing through an index, or by using a simple keyword search. In our E-Librarian Service, the user can enter his question in a very simple and human way; in natural language (NL). Our premise is that more pertinent results would be retrieved if the search engine understood the sense of the user's query. The returned results are then logical consequences of an inference rather than of keyword matchings. Our E-Librarian Service does not return the answer to the user's question, but it retrieves the most pertinent document(s), in which the user finds the answer to his/her question. Among all the documents that have some common information with the user query, our E-Librarian Service identifies the most pertinent match(es), keeping in mind that the user expects an exhaustive answer while preferring a concise answer with only little or no information overhead. Also, our E-Librarian Service always proposes a solution to the user, even if the system concludes that there is no exhaustive answer. Our E-Librarian Service was implemented prototypically in three different educational tools. A first prototype is CHESt (Computer History Expert System); it has a knowledge base with 300 multimedia clips that cover the main events in computer history. A second prototype is MatES (Mathematics Expert System); it has a knowledge base with 115 clips that cover the topic of fractions in mathematics for secondary school w.r.t. the official school programme. All clips were recorded mainly by pupils. The third and most advanced prototype is the "Lecture Butler's E-Librarain Service"; it has a Web service interface to respect a service oriented architecture (SOA), and was developed in the context of the Web-University project at the Hasso-Plattner-Institute (HPI). Two major experiments in an educational environment - at the Lycée Technique Esch/Alzette in Luxembourg - were made to test the pertinence and reliability of our E-Librarian Service as a complement to traditional courses. The first experiment (in 2005) was made with CHESt in different classes, and covered a single lesson. The second experiment (in 2006) covered a period of 6 weeks of intensive use of MatES in one class. There was no classical mathematics lesson where the teacher gave explanations, but the students had to learn in an autonomous and exploratory way. They had to ask questions to the E-Librarian Service just the way they would if there was a human teacher.
Boolean constraint solving technology has made tremendous progress over the last decade, leading to industrial-strength solvers, for example, in the areas of answer set programming (ASP), the constraint satisfaction problem (CSP), propositional satisfiability (SAT) and satisfiability of quantified Boolean formulas (QBF). However, in all these areas, there exist multiple solving strategies that work well on different applications; no strategy dominates all other strategies. Therefore, no individual solver shows robust state-of-the-art performance in all kinds of applications. Additionally, the question arises how to choose a well-performing solving strategy for a given application; this is a challenging question even for solver and domain experts. One way to address this issue is the use of portfolio solvers, that is, a set of different solvers or solver configurations. We present three new automatic portfolio methods: (i) automatic construction of parallel portfolio solvers (ACPP) via algorithm configuration,(ii) solving the $NP$-hard problem of finding effective algorithm schedules with Answer Set Programming (aspeed), and (iii) a flexible algorithm selection framework (claspfolio2) allowing for fair comparison of different selection approaches. All three methods show improved performance and robustness in comparison to individual solvers on heterogeneous instance sets from many different applications. Since parallel solvers are important to effectively solve hard problems on parallel computation systems (e.g., multi-core processors), we extend all three approaches to be effectively applicable in parallel settings. We conducted extensive experimental studies different instance sets from ASP, CSP, MAXSAT, Operation Research (OR), SAT and QBF that indicate an improvement in the state-of-the-art solving heterogeneous instance sets. Last but not least, from our experimental studies, we deduce practical advice regarding the question when to apply which of our methods.
In the last decades, there was a notable progress in solving the well-known Boolean satisfiability (Sat) problem, which can be witnessed by powerful Sat solvers. One of the reasons why these solvers are so fast are structural properties of instances that are utilized by the solver’s interna. This thesis deals with the well-studied structural property treewidth, which measures the closeness of an instance to being a tree. In fact, there are many problems parameterized by treewidth that are solvable in polynomial time in the instance size when parameterized by treewidth.
In this work, we study advanced treewidth-based methods and tools for problems in knowledge representation and reasoning (KR). Thereby, we provide means to establish precise runtime results (upper bounds) for canonical problems relevant to KR. Then, we present a new type of problem reduction, which we call decomposition-guided (DG) that
allows us to precisely monitor the treewidth when reducing from one problem to another problem. This new reduction type will be the basis for a long-open lower bound result for quantified Boolean formulas and allows us to design a new methodology for establishing runtime lower bounds for problems parameterized by treewidth.
Finally, despite these lower bounds, we provide an efficient implementation of algorithms that adhere to treewidth. Our approach finds suitable abstractions of instances, which are subsequently refined in a recursive fashion, and it uses Sat solvers for solving subproblems. It turns out that our resulting solver is quite competitive for two canonical counting problems related to Sat.