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Although Boolean Constraint Technology has made tremendous progress over the last decade, the efficacy of state-of-the-art solvers is known to vary considerably across different types of problem instances, and is known to depend strongly on algorithm parameters. This problem was addressed by means of a simple, yet effective approach using handmade, uniform, and unordered schedules of multiple solvers in ppfolio, which showed very impressive performance in the 2011 Satisfiability Testing (SAT) Competition. Inspired by this, we take advantage of the modeling and solving capacities of Answer Set Programming (ASP) to automatically determine more refined, that is, nonuniform and ordered solver schedules from the existing benchmarking data. We begin by formulating the determination of such schedules as multi-criteria optimization problems and provide corresponding ASP encodings. The resulting encodings are easily customizable for different settings, and the computation of optimum schedules can mostly be done in the blink of an eye, even when dealing with large runtime data sets stemming from many solvers on hundreds to thousands of instances. Also, the fact that our approach can be customized easily enabled us to swiftly adapt it to generate parallel schedules for multi-processor machines.
Manufacturing industries are undergoing a major paradigm shift towards more autonomy. Automated planning and scheduling then becomes a necessity. The Planning and Execution Competition for Logistics Robots in Simulation held at ICAPS is based on this scenario and provides an interesting testbed. However, the posed problem is challenging as also demonstrated by the somewhat weak results in 2017. The domain requires temporal reasoning and dealing with uncertainty. We propose a novel planning system based on Answer Set Programming and the Clingo solver to tackle these problems and incentivize robot cooperation. Our results show a significant performance improvement, both, in terms of lowering computational requirements and better game metrics.
We present the hybrid ASP solver clingcon, combining the simple modeling language and the high performance Boolean solving capacities of Answer Set Programming (ASP) with techniques for using non-Boolean constraints from the area of Constraint Programming (CP). The new clingcon system features an extended syntax supporting global constraints and optimize statements for constraint variables. The major technical innovation improves the interaction between ASP and CP solver through elaborated learning techniques based on irreducible inconsistent sets. A broad empirical evaluation shows that these techniques yield a performance improvement of an order of magnitude.
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.
The use of neural networks is considered as the state of the art in the field of image classification. A large number of different networks are available for this purpose, which, appropriately trained, permit a high level of classification accuracy. Typically, these networks are applied to uncompressed image data, since a corresponding training was also carried out using image data of similar high quality. However, if image data contains image errors, the classification accuracy deteriorates drastically. This applies in particular to coding artifacts which occur due to image and video compression. Typical application scenarios for video compression are narrowband transmission channels for which video coding is required but a subsequent classification is to be carried out on the receiver side. In this paper we present a special H.264/Advanced Video Codec (AVC) based video codec that allows certain regions of a picture to be coded with near constant picture quality in order to allow a reliable classification using neural networks, whereas the remaining image will be coded using constant bit rate. We have combined this feature with the ability to run with lowest latency properties, which is usually also required in remote control applications scenarios. The codec has been implemented as a fully hardwired High Definition video capable hardware architecture which is suitable for Field Programmable Gate Arrays.
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.
We construct a new RC phase shift network based Chua's circuit, which exhibits a period-doubling bifurcation route to chaos. Using coupled versions of such a phase-shift network based Chua's oscillators, we describe a new method for achieving complete synchronization (CS), approximate lag synchronization (LS), and approximate anticipating synchronization (AS) without delay or parameter mismatch. Employing the Pecora and Carroll approach, chaos synchronization is achieved in coupled chaotic oscillators, where the drive system variables control the response system. As a result, AS or LS or CS is demonstrated without using a variable delay line both experimentally and numerically.
Answer Set Programming faces an increasing popularity for problem solving in various domains. While its modeling language allows us to express many complex problems in an easy way, its solving technology enables their effective resolution. In what follows, we detail some of the key factors of its success. Answer Set Programming [ASP; Brewka et al. Commun ACM 54(12):92–103, (2011)] is seeing a rapid proliferation in academia and industry due to its easy and flexible way to model and solve knowledge-intense combinatorial (optimization) problems. To this end, ASP offers a high-level modeling language paired with high-performance solving technology. As a result, ASP systems provide out-off-the-box, general-purpose search engines that allow for enumerating (optimal) solutions. They are represented as answer sets, each being a set of atoms representing a solution. The declarative approach of ASP allows a user to concentrate on a problem’s specification rather than the computational means to solve it. This makes ASP a prime candidate for rapid prototyping and an attractive tool for teaching key AI techniques since complex problems can be expressed in a succinct and elaboration tolerant way. This is eased by the tuning of ASP’s modeling language to knowledge representation and reasoning (KRR). The resulting impact is nicely reflected by a growing range of successful applications of ASP [Erdem et al. AI Mag 37(3):53–68, 2016; Falkner et al. Industrial applications of answer set programming. K++nstliche Intelligenz (2018)]
The course timetabling problem can be generally defined as the task of assigning a number of lectures to a limited set of timeslots and rooms, subject to a given set of hard and soft constraints. The modeling language for course timetabling is required to be expressive enough to specify a wide variety of soft constraints and objective functions. Furthermore, the resulting encoding is required to be extensible for capturing new constraints and for switching them between hard and soft, and to be flexible enough to deal with different formulations. In this paper, we propose to make effective use of ASP as a modeling language for course timetabling. We show that our ASP-based approach can naturally satisfy the above requirements, through an ASP encoding of the curriculum-based course timetabling problem proposed in the third track of the second international timetabling competition (ITC-2007). Our encoding is compact and human-readable, since each constraint is individually expressed by either one or two rules. Each hard constraint is expressed by using integrity constraints and aggregates of ASP. Each soft constraint S is expressed by rules in which the head is the form of penalty (S, V, C), and a violation V and its penalty cost C are detected and calculated respectively in the body. We carried out experiments on four different benchmark sets with five different formulations. We succeeded either in improving the bounds or producing the same bounds for many combinations of problem instances and formulations, compared with the previous best known bounds.
Answer set planning
(2022)
Answer Set Planning refers to the use of Answer Set Programming (ASP) to compute plans, that is, solutions to planning problems, that transform a given state of the world to another state. The development of efficient and scalable answer set solvers has provided a significant boost to the development of ASP-based planning systems. This paper surveys the progress made during the last two and a half decades in the area of answer set planning, from its foundations to its use in challenging planning domains. The survey explores the advantages and disadvantages of answer set planning. It also discusses typical applications of answer set planning and presents a set of challenges for future research.
And/Or reasoning graphs for determining prime implicants in multi-level combinational networks
(1997)
Xenikoudakis et al. report a partial mitochondrial genome of the extinct giant beaver Castoroides and estimate the origin of aquatic behavior in beavers to approximately 20 million years. This time estimate coincides with the extinction of terrestrial beavers and raises the question whether the two events had a common cause.
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.
An introduction to audio content analysis : applications in signal processing and music informatics
(2012)
We address the problem of Finite Model Computation (FMC) of first-order theories and show that FMC can efficiently and transparently be solved by taking advantage of a recent extension of Answer Set Programming (ASP), called incremental Answer Set Programming (iASP). The idea is to use the incremental parameter in iASP programs to account for the domain size of a model. The FMC problem is then successively addressed for increasing domain sizes until an answer set, representing a finite model of the original first-order theory, is found. We implemented a system based on the iASP solver iClingo and demonstrate its competitiveness by showing that it slightly outperforms the winner of the FNT division of CADE's 2009 Automated Theorem Proving (ATP) competition on the respective benchmark collection.
An Extended Query language for action languages (and its application to aggregates and preferences)
(2006)
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.
Algorithm selection (AS) techniques - which involve choosing from a set of algorithms the one expected to solve a given problem instance most efficiently - have substantially improved the state of the art in solving many prominent AI problems, such as SAT, CSP, ASP, MAXSAT and QBF. Although several AS procedures have been introduced, not too surprisingly, none of them dominates all others across all AS scenarios. Furthermore, these procedures have parameters whose optimal values vary across AS scenarios. This holds specifically for the machine learning techniques that form the core of current AS procedures, and for their hyperparameters. Therefore, to successfully apply AS to new problems, algorithms and benchmark sets, two questions need to be answered: (i) how to select an AS approach and (ii) how to set its parameters effectively. We address both of these problems simultaneously by using automated algorithm configuration. Specifically, we demonstrate that we can automatically configure claspfolio 2, which implements a large variety of different AS approaches and their respective parameters in a single, highly-parameterized algorithm framework. Our approach, dubbed AutoFolio, allows researchers and practitioners across a broad range of applications to exploit the combined power of many different AS methods. We demonstrate AutoFolio can significantly improve the performance of claspfolio 2 on 8 out of the 13 scenarios from the Algorithm Selection Library, leads to new state-of-the-art algorithm selectors for 7 of these scenarios, and matches state-of-the-art performance (statistically) on all other scenarios. Compared to the best single algorithm for each AS scenario, AutoFolio achieves average speedup factors between 1.3 and 15.4.
An asymptotic analysis and improvement of AdaBoost in the binary classification case (in Japanese)
(2000)
Institutions are facing the challenge to integrate legacy systems with steadily growing new ones, using different technologies and interaction patterns. With the demand of offering the best potential of all systems, several not matching systems including their functions have to be aggregated and offered in a useable way. This paper presents an adaptive, generalizable and self-organized Personal Learning Environment (PLE) framework with the potential to integrate several heterogeneous services using a service-oriented architecture. First, a general overview over the field is given, followed by the description of the core components of the PLE framework. A prototypical implementation is presented. Finally, it’s shown how the PLE framework can be dynamically adapted to a changing system environment, reflecting experiences from first user studies.
A multiple interpretation scheme is an ordered sequence of morphisms. The ordered multiple interpretation of a word is obtained by concatenating the images of that word in the given order of morphisms. The arbitrary multiple interpretation of a word is the semigroup generated by the images of that word. These interpretations are naturally extended to languages. Four types of ambiguity of multiple interpretation schemata on a language are defined: o-ambiguity, internal ambiguity, weakly external ambiguity and strongly external ambiguity. We investigate the problem of deciding whether a multiple interpretation scheme is ambiguous on regular languages.
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.
The introduction of columnar in-memory databases, along with hardware evolution, has made the execution of transactional and analytical enterprise application workloads on a single system both feasible and viable. Yet, we argue that executing analytical aggregate queries directly on the transactional data can decrease the overall system performance. Despite the aggregation capabilities of columnar in-memory databases, the direct access to records of a materialized aggregate is always more efficient than aggregating on the fly. The traditional approach to materialized aggregates, however, introduces significant overhead in terms of materialized view selection, maintenance, and exploitation. When this overhead is handled by the application, it increases the application complexity, and can slow down the transactional throughput of inserts, updates, and deletes.
In this thesis, we motivate, propose, and evaluate the aggregate cache, a materialized aggregate engine in the main-delta architecture of a columnar in-memory database that provides efficient means to handle costly aggregate queries of enterprise applications. For our design, we leverage the specifics of the main-delta architecture that separates a table into a main and delta partition. The central concept is to only cache the partial aggregate query result as defined on the main partition of a table, because the main partition is relatively stable as records are only inserted into the delta partition. We contribute by proposing incremental aggregate maintenance and query compensation techniques for mixed workloads of enterprise applications. In addition, we introduce aggregate profit metrics that increase the likelihood of persisting the most profitable aggregates in the aggregate cache.
Query compensation and maintenance of materialized aggregates based on joins of multiple tables is expensive due to the partitioned tables in the main-delta architecture. Our analysis of enterprise applications has revealed several data schema and workload patterns. This includes the observation that transactional data is persisted in header and item tables, whereas in many cases, the insertion of related header and item records is executed in a single database transaction. We contribute by proposing an approach to transport these application object semantics to the database system and optimize the query processing using the aggregate cache by applying partition pruning and predicate pushdown techniques.
For the experimental evaluation, we propose the FICO benchmark that is based on data from a productive ERP system with extracted mixed workloads. Our evaluation reveals that the aggregate cache can accelerate the execution of aggregate queries up to a factor of 60 whereas the speedup highly depends on the number of aggregated records in the main and delta partitions. In mixed workloads, the proposed aggregate maintenance and query compensation techniques perform up to an order of magnitude better than traditional materialized aggregate maintenance approaches. The introduced aggregate profit metrics outperform existing costbased metrics by up to 20%. Lastly, the join pruning and predicate pushdown techniques can accelerate query execution in the aggregate cache in the presence of multiple partitioned tables by up to an order of magnitude.
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.