Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of dynamic systems. On the other hand, description logics (DLs) provide a well-suited formalism to describe and reason about static knowledge, used in many areas to specify domain knowledge in an ontology. We investigate how such knowledge can be integrated into the PMC process, introducing ontology-mediated PMC. Specifically, we propose a formalism that links ontologies to dynamic behaviors specified by guarded commands, the de-facto standard input formalism for PMC tools such as Prism. Further, we present and implement a technique for their analysis relying on existing DL-reasoning and PMC tools. This way, we enable the application of standard PMC techniques to analyze knowledge-intensive systems. Our approach is implemented and evaluated on a multi-server system case study, where different DL-ontologies are used to provide specifications of different server platforms and situations the system is executed in.

Computer hardware and software laid the foundation for fundamental innovations in science, technology, economics and society. Novel application areas generate an ever-increasing demand for computation power and storage capacities. Classic CMOS-based hardware and the von Neumann architecture are approaching their limits in miniaturization, power density and communication speed. To meet future demands, researchers work on new device technologies and architecture approaches which in turn require new algorithms and a hardware/software co-design to exploit their capabilities. Since the overall system heterogeneity and complexity increases, the challenge is to build systems with these technologies that are both correct and performant by design. Formal methods in general and model checking in particular are established verification methods in hardware design, and have been successfully applied to many hardware, software and integrated hardware/software systems. In many systems, probabilistic effects arise naturally, e.g., from input patterns, production variations or the occurrence of faults. Probabilistic model checking facilitates the quantitative analysis of performance and reliability measures in stochastic models that formalize this probabilism. The interdisciplinary research project Center for Advancing Electronics Dresden, cfaed for short, aims to explore hardware and software technologies for future information processing systems. It joins the research efforts of different groups working on technologies for all system layers ranging from transistor device research over system architecture up to the application layer. The collaborations among the groups showed a demand for new formal methods and enhanced tools to assist the design and analysis of technologies at all system layers and their cross-layer integration. Addressing these needs is the goal of this thesis. This work contributes to probabilistic model checking for Markovian models with new methods to compute two essential measures in the analysis of hardware/software systems and a method to tackle the state-space explosion problem: 1) Conditional probabilities are well known in stochastic theory and statistics, but efficient methods did not exist to compute conditional expectations in Markov chains and extremal conditional probabilities in Markov decision processes. This thesis develops new polynomial-time algorithms, and it provides a mature implementation for the probabilistic model checker PRISM. 2) Relativized long-run and relativized conditional long-run averages are proposed in this work to reason about probabilities and expectations in Markov chains on the long run when zooming into sets of states or paths. Both types of long-run averages are implemented for PRISM. 3) Symmetry reduction is an effective abstraction technique to tame the state-space explosion problem. However, state-of-the-art probabilistic model checkers apply it only after building the full model and offer no support for specifying non-trivial symmetric components. This thesis fills this gap with a modeling language based on symmetric program graphs that facilitates symmetry reduction on the source level. The new language can be integrated seamlessly into the PRISM modeling language. This work contributes to the research on future hardware/software systems in cfaed with three practical studies that are enabled by the developed methods and their implementations. 1) To confirm relevance of the new methods in practice and to validate the results, the first study analyzes a well-understood synchronization protocol, a test-and-test-and-set spinlock. Beyond this confirmation, the analysis demonstrates the capability to compute properties that are hardly accessible to measurements. 2) Probabilistic write-copy/select is an alternative protocol to overcome the scalability issues of classic resource-locking mechanisms. A quantitative analysis verifies the protocol's principle of operation and evaluates the performance trade-offs to guide future implementations of the protocol. 3) The impact of a new device technology is hard to estimate since circuit-level simulations are not available in the early stages of research. This thesis proposes a formal framework to model and analyze circuit designs for novel transistor technologies. It encompasses an operational model of electrical circuits, a functional model of polarity-controllable transistor devices and algorithms for design space exploration in order to find optimal circuit designs using probabilistic model checking. A practical study assesses the model accuracy for a lab-device based on germanium nanowires and performs an automated exploration and performance analysis of the design space of a given switching function. The experiments demonstrate how the framework enables an early systematic design space exploration and performance evaluation of circuits for experimental transistor devices.:1. Introduction 1.1 Related Work 2. Preliminaries 3. Conditional Probabilities in Markovian Models 3.1 Methods for Discrete- and Continuous-Time Markov Chains 3.2 Reset Method for Markov Decision Processes 3.3 Implementation 3.4 Evaluation and Comparative Studies 3.5 Conclusion 4. Long-Run Averages in Markov Chains 4.1 Relativized Long-Run Average 4.2 Conditional State Evolution 4.3 Implementation 4.4 Conclusion 5. Language-Support for Immediate Symmetry Reduction 5.1 Probabilistic Program Graphs 5.2 Symmetric Probabilistic Program Graphs 5.3 Implementation 5.4 Conclusion 6. Practical Applications of the Developed Techniques 6.1 Test-and-Test-and-Set Spinlock: Quantitative Analysis of an Established Protocol 6.2 Probabilistic Write/Copy-Select: Quantitative Analysis as Design Guide for a Novel Protocol 6.3 Circuit Design for Future Transistor Technologies: Evaluating Polarity-Controllable Multiple-Gate FETs 7. Conclusion Bibliography Appendices A. Conditional Probabilities and Expectations A.1 Selection of Benchmark Models A.2 Additional Benchmark Results A.3 Comparison PRISM vs. Storm B. Language-Support for Immediate Symmetry Reduction B.1 Syntax of the PRISM Modeling Language B.2 Multi-Core Example C. Practical Applications of the Developed Techniques C.1 Test-and-Test-and-Set Spinlock C.2 Probabilistic Write/Copy-Select C.3 Circuit Design for Future Transistor Technologies

The topic of this paper is the determinization problem of ω-automata under the transition-based Emerson-Lei acceptance (called TELA), which generalizes all standard acceptance conditions and is defined using positive Boolean formulas. Such automata can be determinized by first constructing an equivalent generalized Büchi automaton (GBA), which is later determinized. The problem of constructing an equivalent GBA is considered in detail, and three new approaches of solving it are proposed. Furthermore, a new determinization construction is introduced which determinizes several GBA separately and combines them using a product construction. An experimental evaluation shows that the product approach is competitive when compared with state-of-the-art determinization procedures. The second part of the paper studies limit-determinization of TELA and we show that this can be done with a single-exponential blow-up, in contrast to the known double-exponential lower-bound for determinization. Finally, one version of the limit-determinization procedure yields good-for-MDP automata which can be used for quantitative probabilistic model checking.

Mit der steigenden Nachfrage nach Innovationen spielt Software in verschiedenenWirtschaftsbereichen eine wichtige Rolle, wie z.B. in der Automobilindustrie, bei intelligenten Systemen als auch bei Kommunikationssystemen. Daher ist die Qualität für die Softwareentwicklung von großer Bedeutung. Allerdings ändern sich die probabilistische Modelle (die Qualitätsbewertungsmodelle) angesichts der dynamischen Natur moderner Softwaresysteme. Dies führt dazu, dass ihre Übergangswahrscheinlichkeiten im Laufe der Zeit schwanken, welches zu erheblichen Problemen führt. Dahingehend werden probabilistische Modelle im Hinblick auf ihre Laufzeit kontinuierlich aktualisiert. Eine fortdauernde Neubewertung komplexer Wahrscheinlichkeitsmodelle ist jedoch teuer. In letzter Zeit haben sich inkrementelle Ansätze als vielversprechend für die Verifikation von adaptiven Systemen erwiesen. Trotzdem wurden bei der Bewertung struktureller Änderungen im Modell noch keine wesentlichen Verbesserungen erzielt. Wahrscheinlichkeitssysteme werden als Automaten modelliert, wie bei Markov-Modellen. Solche Modelle können in Matrixform dargestellt werden, um die Gleichungen basierend auf Zuständen und Übergangswahrscheinlichkeiten zu lösen. Laufzeitmodelle wie Matrizen sind nicht signifikant, um die Auswirkungen von Modellveränderungen erkennen zu können. In dieser Arbeit wird ein Framework unter Verwendung stochastischer Bäume mit regulären Ausdrücken entwickelt, welches modular aufgebaut ist und eine aktionshaltige sowie probabilistische Logik im Kontext der Modellprüfung aufweist. Ein solches modulares Framework ermöglicht dem Menschen die Entwicklung der Änderungsoperationen für die inkrementelle Berechnung lokaler Änderungen, die im Modell auftreten können. Darüber hinaus werden probabilistische Änderungsmuster beschrieben, um eine effiziente inkrementelle Verifizierung, unter Verwendung von Bäumen mit regulären Ausdrücken, anwenden zu können. Durch die Bewertung der Ergebnisse wird der Vorgang abgeschlossen. / Software plays an innovative role in many different domains, such as car industry, autonomous and smart systems, and communication. Hence, the quality of the software is of utmost importance and needs to be properly addressed during software evolution. Several approaches have been developed to evaluate systems’ quality attributes, such as reliability, safety, and performance of software. Due to the dynamic nature of modern software systems, probabilistic models representing the quality of the software and their transition probabilities change over time and fluctuate, leading to a significant problem that needs to be solved to obtain correct evaluation results of quantitative properties. Probabilistic models need to be continually updated at run-time to solve this issue. However, continuous re-evaluation of complex probabilistic models is expensive. Recently, incremental approaches have been found to be promising for the verification of evolving and self-adaptive systems. Nevertheless, substantial improvements have not yet been achieved for evaluating structural changes in the model. Probabilistic systems are usually represented in a matrix form to solve the equations based on states and transition probabilities. On the other side, evolutionary changes can create various effects on theese models and force them to re-verify the whole system. Run-time models, such as matrices or graph representations, lack the expressiveness to identify the change effect on the model. In this thesis, we develop a framework using stochastic regular expression trees, which are modular, with action-based probabilistic logic in the model checking context. Such a modular framework enables us to develop change operations for the incremental computation of local changes that can occur in the model. Furthermore, we describe probabilistic change patterns to apply efficient incremental quantitative verification using stochastic regular expression trees and evaluate our results.