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Institute
- Institut für Informatik und Computational Science (1110) (remove)
Reliable and robust data processing is one of the hardest requirements for systems in fields such as medicine, security, automotive, aviation, and space, to prevent critical system failures caused by changes in operating or environmental conditions. In particular, Signal Integrity (SI) effects such as crosstalk may distort the signal information in sensitive mixed-signal designs. A challenge for hardware systems used in the space are radiation effects. Namely, Single Event Effects (SEEs) induced by high-energy particle hits may lead to faulty computation, corrupted configuration settings, undesired system behavior, or even total malfunction.
Since these applications require an extra effort in design and implementation, it is beneficial to master the standard cell design process and corresponding design flow methodologies optimized for such challenges. Especially for reliable, low-noise differential signaling logic such as Current Mode Logic (CML), a digital design flow is an orthogonal approach compared to traditional manual design. As a consequence, mandatory preliminary considerations need to be addressed in more detail. First of all, standard cell library concepts with suitable cell extensions for reliable systems and robust space applications have to be elaborated. Resulting design concepts at the cell level should enable the logical synthesis for differential logic design or improve the radiation-hardness. In parallel, the main objectives of the proposed cell architectures are to reduce the occupied area, power, and delay overhead. Second, a special setup for standard cell characterization is additionally required for a proper and accurate logic gate modeling. Last but not least, design methodologies for mandatory design flow stages such as logic synthesis and place and route need to be developed for the respective hardware systems to keep the reliability or the radiation-hardness at an acceptable level.
This Thesis proposes and investigates standard cell-based design methodologies and techniques for reliable and robust hardware systems implemented in a conventional semi-conductor technology. The focus of this work is on reliable differential logic design and robust radiation-hardening-by-design circuits. The synergistic connections of the digital design flow stages are systematically addressed for these two types of hardware systems. In more detail, a library for differential logic is extended with single-ended pseudo-gates for intermediate design steps to support the logic synthesis and layout generation with commercial Computer-Aided Design (CAD) tools. Special cell layouts are proposed to relax signal routing. A library set for space applications is similarly extended by novel Radiation-Hardening-by-Design (RHBD) Triple Modular Redundancy (TMR) cells, enabling a one fault correction. Therein, additional optimized architectures for glitch filter cells, robust scannable and self-correcting flip-flops, and clock-gates are proposed. The circuit concepts and the physical layout representation views of the differential logic gates and the RHBD cells are discussed. However, the quality of results of designs depends implicitly on the accuracy of the standard cell characterization which is examined for both types therefore. The entire design flow is elaborated from the hardware design description to the layout representations. A 2-Phase routing approach together with an intermediate design conversion step is proposed after the initial place and route stage for reliable, pure differential designs, whereas a special constraining for RHBD applications in a standard technology is presented.
The digital design flow for differential logic design is successfully demonstrated on a reliable differential bipolar CML application. A balanced routing result of its differential signal pairs is obtained by the proposed 2-Phase-routing approach. Moreover, the elaborated standard cell concepts and design methodology for RHBD circuits are applied to the digital part of a 7.5-15.5 MSPS 14-bit Analog-to-Digital Converter (ADC) and a complex microcontroller architecture. The ADC is implemented in an unhardened standard semiconductor technology and successfully verified by electrical measurements. The overhead of the proposed hardening approach is additionally evaluated by design exploration of the microcontroller application. Furthermore, the first obtained related measurement results of novel RHBD-∆TMR flip-flops show a radiation-tolerance up to a threshold Linear Energy Transfer (LET) of 46.1, 52.0, and 62.5 MeV cm2 mg-1 and savings in silicon area of 25-50 % for selected TMR standard cell candidates.
As a conclusion, the presented design concepts at the cell and library levels, as well as the design flow modifications are adaptable and transferable to other technology nodes. In particular, the design of hybrid solutions with integrated reliable differential logic modules together with robust radiation-tolerant circuit parts is enabled by the standard cell concepts and design methods proposed in this work.
As a result of CMOS scaling, radiation-induced Single-Event Effects (SEEs) in electronic circuits became a critical reliability issue for modern Integrated Circuits (ICs) operating under harsh radiation conditions. SEEs can be triggered in combinational or sequential logic by the impact of high-energy particles, leading to destructive or non-destructive faults, resulting in data corruption or even system failure. Typically, the SEE mitigation methods are deployed statically in processing architectures based on the worst-case radiation conditions, which is most of the time unnecessary and results in a resource overhead. Moreover, the space radiation conditions are dynamically changing, especially during Solar Particle Events (SPEs). The intensity of space radiation can differ over five orders of magnitude within a few hours or days, resulting in several orders of magnitude fault probability variation in ICs during SPEs. This thesis introduces a comprehensive approach for designing a self-adaptive fault resilient multiprocessing system to overcome the static mitigation overhead issue. This work mainly addresses the following topics: (1) Design of on-chip radiation particle monitor for real-time radiation environment detection, (2) Investigation of space environment predictor, as support for solar particle events forecast, (3) Dynamic mode configuration in the resilient multiprocessing system. Therefore, according to detected and predicted in-flight space radiation conditions, the target system can be configured to use no mitigation or low-overhead mitigation during non-critical periods of time. The redundant resources can be used to improve system performance or save power. On the other hand, during increased radiation activity periods, such as SPEs, the mitigation methods can be dynamically configured appropriately depending on the real-time space radiation environment, resulting in higher system reliability. Thus, a dynamic trade-off in the target system between reliability, performance and power consumption in real-time can be achieved. All results of this work are evaluated in a highly reliable quad-core multiprocessing system that allows the self-adaptive setting of optimal radiation mitigation mechanisms during run-time. Proposed methods can serve as a basis for establishing a comprehensive self-adaptive resilient system design process. Successful implementation of the proposed design in the quad-core multiprocessor shows its application perspective also in the other designs.
Large-scale databases that report the inhibitory capacities of many combinations of candidate drug compounds and cultivated cancer cell lines have driven the development of preclinical drug-sensitivity models based on machine learning. However, cultivated cell lines have devolved from human cancer cells over years or even decades under selective pressure in culture conditions. Moreover, models that have been trained on in vitro data cannot account for interactions with other types of cells. Drug-response data that are based on patient-derived cell cultures, xenografts, and organoids, on the other hand, are not available in the quantities that are needed to train high-capacity machine-learning models. We found that pre-training deep neural network models of drug sensitivity on in vitro drug-sensitivity databases before fine-tuning the model parameters on patient-derived data improves the models’ accuracy and improves the biological plausibility of the features, compared to training only on patient-derived data. From our experiments, we can conclude that pre-trained models outperform models that have been trained on the target domains in the vast majority of cases.
Answer Set Programming (ASP) is a paradigm for modeling and solving problems for knowledge representation and reasoning. There are plenty of results dedicated to studying the hardness of (fragments of) ASP. So far, these studies resulted in characterizations in terms of computational complexity as well as in fine-grained insights presented in form of dichotomy-style results, lower bounds when translating to other formalisms like propositional satisfiability (SAT), and even detailed parameterized complexity landscapes. A generic parameter in parameterized complexity originating from graph theory is the socalled treewidth, which in a sense captures structural density of a program. Recently, there was an increase in the number of treewidth-based solvers related to SAT. While there are translations from (normal) ASP to SAT, no reduction that preserves treewidth or at least keeps track of the treewidth increase is known. In this paper we propose a novel reduction from normal ASP to SAT that is aware of the treewidth, and guarantees that a slight increase of treewidth is indeed sufficient. Further, we show a new result establishing that, when considering treewidth, already the fragment of normal ASP is slightly harder than SAT (under reasonable assumptions in computational complexity). This also confirms that our reduction probably cannot be significantly improved and that the slight increase of treewidth is unavoidable. Finally, we present an empirical study of our novel reduction from normal ASP to SAT, where we compare treewidth upper bounds that are obtained via known decomposition heuristics. Overall, our reduction works better with these heuristics than existing translations. (c) 2021 Elsevier B.V. All rights reserved.
The highly structured nature of the educational sector demands effective policy mechanisms close to the needs of the field. That is why evidence-based policy making, endorsed by the European Commission under Erasmus+ Key Action 3, aims to make an alignment between the domains of policy and practice. Against this background, this article addresses two issues: First, that there is a vertical gap in the translation of higher-level policies to local strategies and regulations. Second, that there is a horizontal gap between educational domains regarding the policy awareness of individual players. This was analyzed in quantitative and qualitative studies with domain experts from the fields of virtual mobility and teacher training. From our findings, we argue that the combination of both gaps puts the academic bridge from secondary to tertiary education at risk, including the associated knowledge proficiency levels. We discuss the role of digitalization in the academic bridge by asking the question: which value does the involved stakeholders expect from educational policies? As a theoretical basis, we rely on the model of value co-creation for and by stakeholders. We describe the used instruments along with the obtained results and proposed benefits. Moreover, we reflect on the methodology applied, and we finally derive recommendations for future academic bridge policies.
Accurately solving classification problems nowadays is likely to be the most relevant machine learning task. Binary classification separating two classes only is algorithmically simpler but has fewer potential applications as many real-world problems are multi-class. On the reverse, separating only a subset of classes simplifies the classification task. Even though existing multi-class machine learning algorithms are very flexible regarding the number of classes, they assume that the target set Y is fixed and cannot be restricted once the training is finished. On the other hand, existing state-of-the-art production environments are becoming increasingly interconnected with the advance of Industry 4.0 and related technologies such that additional information can simplify the respective classification problems. In light of this, the main aim of this thesis is to introduce dynamic classification that generalizes multi-class classification such that the target class set can be restricted arbitrarily to a non-empty class subset M of Y at any time between two consecutive predictions.
This task is solved by a combination of two algorithmic approaches. First, classifier calibration, which transforms predictions into posterior probability estimates that are intended to be well calibrated. The analysis provided focuses on monotonic calibration and in particular corrects wrong statements that appeared in the literature. It also reveals that bin-based evaluation metrics, which became popular in recent years, are unjustified and should not be used at all. Next, the validity of Platt scaling, which is the most relevant parametric calibration approach, is analyzed in depth. In particular, its optimality for classifier predictions distributed according to four different families of probability distributions as well its equivalence with Beta calibration up to a sigmoidal preprocessing are proven. For non-monotonic calibration, extended variants on kernel density estimation and the ensemble method EKDE are introduced. Finally, the calibration techniques are evaluated using a simulation study with complete information as well as on a selection of 46 real-world data sets.
Building on this, classifier calibration is applied as part of decomposition-based classification that aims to reduce multi-class problems to simpler (usually binary) prediction tasks. For the involved fusing step performed at prediction time, a new approach based on evidence theory is presented that uses classifier calibration to model mass functions. This allows the analysis of decomposition-based classification against a strictly formal background and to prove closed-form equations for the overall combinations. Furthermore, the same formalism leads to a consistent integration of dynamic class information, yielding a theoretically justified and computationally tractable dynamic classification model. The insights gained from this modeling are combined with pairwise coupling, which is one of the most relevant reduction-based classification approaches, such that all individual predictions are combined with a weight. This not only generalizes existing works on pairwise coupling but also enables the integration of dynamic class information.
Lastly, a thorough empirical study is performed that compares all newly introduced approaches to existing state-of-the-art techniques. For this, evaluation metrics for dynamic classification are introduced that depend on corresponding sampling strategies. Thereafter, these are applied during a three-part evaluation. First, support vector machines and random forests are applied on 26 data sets from the UCI Machine Learning Repository. Second, two state-of-the-art deep neural networks are evaluated on five benchmark data sets from a relatively recent reference work. Here, computationally feasible strategies to apply the presented algorithms in combination with large-scale models are particularly relevant because a naive application is computationally intractable. Finally, reference data from a real-world process allowing the inclusion of dynamic class information are collected and evaluated. The results show that in combination with support vector machines and random forests, pairwise coupling approaches yield the best results, while in combination with deep neural networks, differences between the different approaches are mostly small to negligible. Most importantly, all results empirically confirm that dynamic classification succeeds in improving the respective prediction accuracies. Therefore, it is crucial to pass dynamic class information in respective applications, which requires an appropriate digital infrastructure.
Large-scale databases that report the inhibitory capacities of many combinations of candidate drug compounds and cultivated cancer cell lines have driven the development of preclinical drug-sensitivity models based on machine learning. However, cultivated cell lines have devolved from human cancer cells over years or even decades under selective pressure in culture conditions. Moreover, models that have been trained on in vitro data cannot account for interactions with other types of cells. Drug-response data that are based on patient-derived cell cultures, xenografts, and organoids, on the other hand, are not available in the quantities that are needed to train high-capacity machine-learning models. We found that pre-training deep neural network models of drug sensitivity on in vitro drug-sensitivity databases before fine-tuning the model parameters on patient-derived data improves the models’ accuracy and improves the biological plausibility of the features, compared to training only on patient-derived data. From our experiments, we can conclude that pre-trained models outperform models that have been trained on the target domains in the vast majority of cases.
The highly structured nature of the educational sector demands effective policy mechanisms close to the needs of the field. That is why evidence-based policy making, endorsed by the European Commission under Erasmus+ Key Action 3, aims to make an alignment between the domains of policy and practice. Against this background, this article addresses two issues: First, that there is a vertical gap in the translation of higher-level policies to local strategies and regulations. Second, that there is a horizontal gap between educational domains regarding the policy awareness of individual players. This was analyzed in quantitative and qualitative studies with domain experts from the fields of virtual mobility and teacher training. From our findings, we argue that the combination of both gaps puts the academic bridge from secondary to tertiary education at risk, including the associated knowledge proficiency levels. We discuss the role of digitalization in the academic bridge by asking the question: which value does the involved stakeholders expect from educational policies? As a theoretical basis, we rely on the model of value co-creation for and by stakeholders. We describe the used instruments along with the obtained results and proposed benefits. Moreover, we reflect on the methodology applied, and we finally derive recommendations for future academic bridge policies.
Lehrende in der Lehrkräfteausbildung sind stets damit konfrontiert, dass sie den Studierenden innovative Methoden modernen Schulunterrichts traditionell rezipierend vorstellen. In Deutschland gibt es circa 40 Universitäten, die Informatik mit Lehramtsbezug ausbilden. Allerdings gibt es nur wenige Konzepte, die sich mit der Verbindung von Bildungswissenschaften und der Informatik mit ihrer Didaktik beschäftigen und keine Konzepte, die eine konstruktivistische Lehre in der Informatik verfolgen.
Daher zielt diese Masterarbeit darauf ab, diese Lücke aufgreifen und anhand des „Didaktik der Informatik I“ Moduls der Universität Potsdam ein Modell zur konstruktivistischen Hochschullehre zu entwickeln. Dabei soll ein bestehendes konstruktivistisches Lehrmodell auf die Informatikdidaktik übertragen und Elemente zur Verbindung von Bildungswissenschaften, Fachwissenschaften und Fachdidaktiken mit einbezogen werden. Dies kann eine Grundlage für die Planung von Informatikdidaktischen Modulen bieten, aber auch als Inspiration zur Übertragung bestehender innovativer Lehrkonzepte auf andere Fachdidaktiken dienen.
Um ein solches konstruktivistisches Lehr-Lern-Modell zu erstellen, wird zunächst der Zusammenhang von Bildungswissenschaften, Fachwissenschaften und Fachdidaktiken erläutert und anschließend die Notwendigkeit einer Vernetzung hervorgehoben. Hieran folgt eine Darstellung zu relevanten Lerntheorien und bereits entwickelten innovativen Lernkonzepten. Anknüpfend wird darauf eingegangen, welche Anforderungen die Kultusminister- Konferenz an die Ausbildung von Lehrkräften stellt und wie diese Ausbildung für die Informatik momentan an der Universität Potsdam erfolgt. Aus allen Erkenntnissen heraus werden Anforderungen an ein konstruktivistisches Lehrmodell festgelegt. Unter Berücksichtigung der Voraussetzungen der Studienordnung für das Lehramt Informatik wird anschließend ein Modell für konstruktivistische Informatikdidaktik vorgestellt.
Weiterführende Forschung könnte sich damit auseinandersetzen, inwiefern sich die Motivation und Leistung im vergleich zum ursprünglichen Modul ändert und ob die Kompetenzen zur Unterrichtsplanung und Unterrichtsgestaltung durch das neue Modulkonzept stärker ausgebaut werden können.
Continuous verification of network security compliance is an accepted need. Especially, the analysis of stateful packet filters plays a central role for network security in practice. But the few existing tools which support the analysis of stateful packet filters are based on general applicable formal methods like Satifiability Modulo Theories (SMT) or theorem prover and show runtimes in the order of minutes to hours making them unsuitable for continuous compliance verification. In this work, we address these challenges and present the concept of state shell interweaving to transform a stateful firewall rule set into a stateless rule set. This allows us to reuse any fast domain specific engine from the field of data plane verification tools leveraging smart, very fast, and domain specialized data structures and algorithms including Header Space Analysis (HSA). First, we introduce the formal language FPL that enables a high-level human-understandable specification of the desired state of network security. Second, we demonstrate the instantiation of a compliance process using a verification framework that analyzes the configuration of complex networks and devices - including stateful firewalls - for compliance with FPL policies. Our evaluation results show the scalability of the presented approach for the well known Internet2 and Stanford benchmarks as well as for large firewall rule sets where it outscales state-of-the-art tools by a factor of over 41.
Computational drug sensitivity models have the potential to improve therapeutic outcomes by identifying targeted drug components that are likely to achieve the highest efficacy for a cancer cell line at hand at a therapeutic dose. State of the art drug sensitivity models use regression techniques to predict the inhibitory concentration of a drug for a tumor cell line. This regression objective is not directly aligned with either of these principal goals of drug sensitivity models: We argue that drug sensitivity modeling should be seen as a ranking problem with an optimization criterion that quantifies a drug's inhibitory capacity for the cancer cell line at hand relative to its toxicity for healthy cells. We derive an extension to the well-established drug sensitivity regression model PaccMann that employs a ranking loss and focuses on the ratio of inhibitory concentration and therapeutic dosage range. We find that the ranking extension significantly enhances the model's capability to identify the most effective anticancer drugs for unseen tumor cell profiles based in on in-vitro data.
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.
In this paper, we present a study comparing the depth to diameter (d/D) ratio of small simple craters (200-1000 m) of an area between -88.5 degrees to -90 degrees latitude at the lunar south pole containing Permanent Shadowed Regions (PSRs) versus craters without PSRs. As PSRs can reach temperatures of 110 K and are capable of harboring volatiles, especially water ice, we analyzed the relationship of depth versus diameter ratios and its possible implications for harboring water ice. Variations in the d/D ratios can also be caused by other processes such as degradation, isostatic adjustment, or differences in surface properties. The conducted d/D ratio analysis suggests that a differentiation between craters containing PSRs versus craters without PSRs occurs. Thus, a possible direct relation between d/D ratio, PSRs, and water ice harboring might exist. Our results suggest that differences in the target's surface properties may explain the obtained results. The resulting d/D ratios of craters with PSRs can help to select target areas for future In-Situ Resource Utilization (ISRU) missions.
Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing deep metric learning techniques, the embedding of an instance is given by a feature vector produced by a deep neural network and Euclidean distance or cosine similarity defines distances between these vectors. This paper studies deep distributional embeddings of sequences, where the embedding of a sequence is given by the distribution of learned deep features across the sequence. The motivation for this is to better capture statistical information about the distribution of patterns within the sequence in the embedding. When embeddings are distributions rather than vectors, measuring distances between embeddings involves comparing their respective distributions. The paper therefore proposes a distance metric based on Wasserstein distances between the distributions and a corresponding loss function for metric learning, which leads to a novel end-to-end trainable embedding model. We empirically observe that distributional embeddings outperform standard vector embeddings and that training with the proposed Wasserstein metric outperforms training with other distance functions.
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.
Objectives To compare image quality of deep learning reconstruction (AiCE) for radiomics feature extraction with filtered back projection (FBP), hybrid iterative reconstruction (AIDR 3D), and model-based iterative reconstruction (FIRST). Methods Effects of image reconstruction on radiomics features were investigated using a phantom that realistically mimicked a 65-year-old patient's abdomen with hepatic metastases. The phantom was scanned at 18 doses from 0.2 to 4 mGy, with 20 repeated scans per dose. Images were reconstructed with FBP, AIDR 3D, FIRST, and AiCE. Ninety-three radiomics features were extracted from 24 regions of interest, which were evenly distributed across three tissue classes: normal liver, metastatic core, and metastatic rim. Features were analyzed in terms of their consistent characterization of tissues within the same image (intraclass correlation coefficient >= 0.75), discriminative power (Kruskal-Wallis test p value < 0.05), and repeatability (overall concordance correlation coefficient >= 0.75). Results The median fraction of consistent features across all doses was 6%, 8%, 6%, and 22% with FBP, AIDR 3D, FIRST, and AiCE, respectively. Adequate discriminative power was achieved by 48%, 82%, 84%, and 92% of features, and 52%, 20%, 17%, and 39% of features were repeatable, respectively. Only 5% of features combined consistency, discriminative power, and repeatability with FBP, AIDR 3D, and FIRST versus 13% with AiCE at doses above 1 mGy and 17% at doses >= 3 mGy. AiCE was the only reconstruction technique that enabled extraction of higher-order features. Conclusions AiCE more than doubled the yield of radiomics features at doses typically used clinically. Inconsistent tissue characterization within CT images contributes significantly to the poor stability of radiomics features.
Programs are often subjected to significant optimizing and parallelizing transformations based on extensive dependence analysis. Formal validation of such transformations needs modelling paradigms which can capture both control and data dependences in the program vividly. Being value-based with an inherent scope of capturing parallelism, the untimed coloured Petri net (CPN) models, reported in the literature, fit the bill well; accordingly, they are likely to be more convenient as the intermediate representations (IRs) of both the source and the transformed codes for translation validation than strictly sequential variable-based IRs like sequential control flow graphs (CFGs). In this work, an efficient path-based equivalence checking method for CPN models of programs on integers is presented. Extensive experimentation has been carried out on several sequential and parallel examples. Complexity and correctness issues have been treated rigorously for the method.
The intensity of cosmic radiation may differ over five orders of magnitude within a few hours or days during the Solar Particle Events (SPEs), thus increasing for several orders of magnitude the probability of Single Event Upsets (SEUs) in space-borne electronic systems. Therefore, it is vital to enable the early detection of the SEU rate changes in order to ensure timely activation of dynamic radiation hardening measures. In this paper, an embedded approach for the prediction of SPEs and SRAM SEU rate is presented. The proposed solution combines the real-time SRAM-based SEU monitor, the offline-trained machine learning model and online learning algorithm for the prediction. With respect to the state-of-the-art, our solution brings the following benefits: (1) Use of existing on-chip data storage SRAM as a particle detector, thus minimizing the hardware and power overhead, (2) Prediction of SRAM SEU rate one hour in advance, with the fine-grained hourly tracking of SEU variations during SPEs as well as under normal conditions, (3) Online optimization of the prediction model for enhancing the prediction accuracy during run-time, (4) Negligible cost of hardware accelerator design for the implementation of selected machine learning model and online learning algorithm. The proposed design is intended for a highly dependable and self-adaptive multiprocessing system employed in space applications, allowing to trigger the radiation mitigation mechanisms before the onset of high radiation levels.
We present a method employing Answer Set Programming in combination with Approximate Model Counting for fast and accurate calculation of error propagation probabilities in digital circuits. By an efficient problem encoding, we achieve an input data format similar to a Verilog netlist so that extensive preprocessing is avoided. By a tight interconnection of our application with the underlying solver, we avoid iterating over fault sites and reduce calls to the solver. Several circuits were analyzed with varying numbers of considered cycles and different degrees of approximation. Our experiments show, that the runtime can be reduced by approximation by a factor of 91, whereas the error compared to the exact result is below 1%.