On the analysis of stochastic timed systems

The formal methods approach to develop reliable and efficient safety- or performance-critical systems is to construct mathematically precise models of such systems on which properties of interest, such as safety guarantees or performance requirements, can be verified automatically. In this thesis, we present techniques that extend the reach of exhaustive and statistical model checking to verify reachability and reward-based properties of compositional behavioural models that support quantitative aspects such as real time and randomised decisions. We present two techniques that allow sound statistical model checking for the nondeterministic-randomised model of Markov decision processes. We investigate the relationship between two different definitions of the model of probabilistic timed automata, as well as potential ways to apply statistical model checking. Stochastic timed automata allow nondeterministic choices as well as nondeterministic and stochastic delays, and we present the first exhaustive model checking algorithm that allows their analysis. All the approaches introduced in this thesis are implemented as part of the Modest Toolset, which supports the construction and verification of models specified in the formal modelling language Modest. We conclude by applying this language and toolset to study novel distributed control strategies for photovoltaic microgenerators

An Overview of Modest Models and Tools for Real Stochastic Timed Systems

We depend on the safe, reliable, and timely operation of cyber-physical systems ranging from smart grids to avionics components. Many of them involve time-dependent behaviours and are subject to randomness. Modelling languages and verification tools thus need to support these quantitative aspects. In my invited presentation at MARS 2022, I gave an introduction to quantitative verification using the Modest modelling language and the Modest Toolset, and highlighted three recent case studies with increasing demands on model expressiveness and tool capabilities: A case of power supply noise in a network-on-chip modelled as a Markov chain; a case of message routing in satellite constellations that uses Markov decision processes with distributed information; and a case of optimising an attack on Bitcoin via Markov automata model checking. This paper summarises the presentation.Comment: In Proceedings MARS 2022, arXiv:2203.0929

Correct Probabilistic Model Checking with Floating-Point Arithmetic

Probabilistic model checking computes probabilities and expected values related to designated behaviours of interest in Markov models. As a formal verification approach, it is applied to critical systems; thus we trust that probabilistic model checkers deliver correct results. To achieve scalability and performance, however, these tools use finite-precision floating-point numbers to represent and calculate probabilities and other values. As a consequence, their results are affected by rounding errors that may accumulate and interact in hard-to-predict ways. In this paper, we show how to implement fast and correct probabilistic model checking by exploiting the ability of current hardware to control the direction of rounding in floating-point calculations. We outline the complications in achieving correct rounding from higher-level programming languages, describe our implementation as part of the Modest Toolset's 'mcsta' model checker, and exemplify the tradeoffs between performance and correctness in an extensive experimental evaluation across different operating systems and CPU architectures

On-the-fly confluence detection for statistical model checking (extended version)

Statistical model checking is an analysis method that circumvents the state space explosion problem in model-based verification by combining probabilistic simulation with statistical methods that provide clear error bounds. As a simulation-based technique, it can only provide sound results if the underlying model is a stochastic process. In verification, however, models are usually variations of nondeterministic transition systems. The notion of confluence allows the reduction of such transition systems in classical model checking by removing spurious nondeterministic choices. In this paper, we show that confluence can be adapted to detect and discard such choices on-the-fly during simulation, thus extending the applicability of statistical model checking to a subclass of Markov decision processes. In contrast to previous approaches that use partial order reduction, the confluence-based technique can handle additional kinds of nondeterminism. In particular, it is not restricted to interleavings. We evaluate our approach, which is implemented as part of the modes simulator for the Modest modelling language, on a set of examples that highlight its strengths and limitations and show the improvements compared to the partial order-based method

On the analysis of stochastic timed systems

The formal methods approach to develop reliable and efficient safety- or performance-critical systems is to construct mathematically precise models of such systems on which properties of interest, such as safety guarantees or performance requirements, can be verified automatically. In this thesis, we present techniques that extend the reach of exhaustive and statistical model checking to verify reachability and reward-based properties of compositional behavioural models that support quantitative aspects such as real time and randomised decisions. We present two techniques that allow sound statistical model checking for the nondeterministic-randomised model of Markov decision processes. We investigate the relationship between two different definitions of the model of probabilistic timed automata, as well as potential ways to apply statistical model checking. Stochastic timed automata allow nondeterministic choices as well as nondeterministic and stochastic delays, and we present the first exhaustive model checking algorithm that allows their analysis. All the approaches introduced in this thesis are implemented as part of the Modest Toolset, which supports the construction and verification of models specified in the formal modelling language Modest. We conclude by applying this language and toolset to study novel distributed control strategies for photovoltaic microgenerators.Formale Methoden erlauben die Entwicklung verlässlicher und performanter sicherheits- oder zeitkritischer Systeme, indem auf mathematisch präzisen Modellen relevante Eigenschaften wie Sicherheits- oder Performance-Garantien automatisch verifiziert werden. In dieser Dissertation stellen wir Methoden vor, mit denen die Anwendbarkeit der klassischen und statistischen Modellprüfung (model checking) zur Verifikation von Erreichbarkeits- und Nutzenseigenschaften auf kompositionellen Verhaltensmodellen, die quantitative Aspekte wie zufallsbasierte Entscheidungen und Echtzeitverhalten enthalten, erweitert wird. Wir zeigen zwei Methoden auf, die eine korrekte statistische Modellprüfung von Markov-Entscheidungsprozessen erlauben. Wir untersuchen den Zusammenhang zwischen zwei Definitionen des Modells des probabilistischen Zeitautomaten sowie mögliche Wege, die statistische Modellprüfung auf diese Art Modelle anzuwenden. Stochastische Zeitautomaten erlauben nichtdeterministische Entscheidungen sowie nichtdeterministische und stochastische Wartezeiten; wir stellen den ersten Algorithmus für die klassische Modellprüfung dieser Automaten vor. Alle Techniken, die wir in dieser Dissertation behandeln, sind als Teil des Modest Toolsets, welches die Erstellung und Verifikation von Modellen mittels der formalen Modellierungssprache Modest erlaubt, implementiert. Wir verwenden diese Sprache und Tools, um neuartige verteilte Steuerungsalgorithmen für Photovoltaikanlagen zu untersuchen

Optimistic Value Iteration

Markov decision processes are widely used for planning and verification in settings that combine controllable or adversarial choices with probabilistic behaviour. The standard analysis algorithm, value iteration, only provides a lower bound on unbounded probabilities or reward values. Two "sound" variations, which also deliver an upper bound, have recently appeared. In this paper, we present optimistic value iteration, a new sound approach that leverages value iteration's ability to usually deliver tight lower bounds: we obtain a lower bound via standard value iteration, use the result to "guess" an upper bound, and prove the latter's correctness. Optimistic value iteration is easy to implement, does not require extra precomputations or a priori state space transformations, and works for computing reachability probabilities as well as expected rewards. It is also fast, as we show via an extensive experimental evaluation using our publicly available implementation within the Modest Toolset