Fair Termination of Binary Sessions

A binary session is a private communication channel that connects two processes, each adhering to a protocol description called session type. In this work, we study the first type system that ensures the fair termination of binary sessions. A session fairly terminates if all of the infinite executions admitted by its protocol are deemed ‘unrealistic’ because they violate certain fairness assumptions. Fair termination entails the eventual completion of all pending input/output actions, including those that depend on the completion of an unbounded number of other actions in possibly different sessions. This form of lock freedom allows us to address a large family of natural communication patterns that fall outside the scope of existing type systems. Our type system is also the first to adopt fair subtyping, a liveness-preserving refinement of the standard subtyping relation for session types that so far has only been studied theoretically. Fair subtyping is surprisingly subtle not only to characterize concisely but also to use appropriately, to the point that the type system must carefully account for all usages of fair subtyping to avoid compromising its liveness-preserving properties

On Irrelevance and Algorithmic Equality in Predicative Type Theory

Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model.Comment: 36 pages, superseds the FoSSaCS 2011 paper of the first author, titled "Irrelevance in Type Theory with a Heterogeneous Equality Judgement

On the connection of probabilistic model checking, planning, and learning for system verification

This thesis presents approaches using techniques from the model checking, planning, and learning community to make systems more reliable and perspicuous. First, two heuristic search and dynamic programming algorithms are adapted to be able to check extremal reachability probabilities, expected accumulated rewards, and their bounded versions, on general Markov decision processes (MDPs). Thereby, the problem space originally solvable by these algorithms is enlarged considerably. Correctness and optimality proofs for the adapted algorithms are given, and in a comprehensive case study on established benchmarks it is shown that the implementation, called Modysh, is competitive with state-of-the-art model checkers and even outperforms them on very large state spaces. Second, Deep Statistical Model Checking (DSMC) is introduced, usable for quality assessment and learning pipeline analysis of systems incorporating trained decision-making agents, like neural networks (NNs). The idea of DSMC is to use statistical model checking to assess NNs resolving nondeterminism in systems modeled as MDPs. The versatility of DSMC is exemplified in a number of case studies on Racetrack, an MDP benchmark designed for this purpose, flexibly modeling the autonomous driving challenge. In a comprehensive scalability study it is demonstrated that DSMC is a lightweight technique tackling the complexity of NN analysis in combination with the state space explosion problem.Diese Arbeit präsentiert Ansätze, die Techniken aus dem Model Checking, Planning und Learning Bereich verwenden, um Systeme verlässlicher und klarer verständlich zu machen. Zuerst werden zwei Algorithmen für heuristische Suche und dynamisches Programmieren angepasst, um Extremwerte für Erreichbarkeitswahrscheinlichkeiten, Erwartungswerte für Kosten und beschränkte Varianten davon, auf generellen Markov Entscheidungsprozessen (MDPs) zu untersuchen. Damit wird der Problemraum, der ursprünglich mit diesen Algorithmen gelöst wurde, deutlich erweitert. Korrektheits- und Optimalitätsbeweise für die angepassten Algorithmen werden gegeben und in einer umfassenden Fallstudie wird gezeigt, dass die Implementierung, namens Modysh, konkurrenzfähig mit den modernsten Model Checkern ist und deren Leistung auf sehr großen Zustandsräumen sogar übertrifft. Als Zweites wird Deep Statistical Model Checking (DSMC) für die Qualitätsbewertung und Lernanalyse von Systemen mit integrierten trainierten Entscheidungsgenten, wie z.B. neuronalen Netzen (NN), eingeführt. Die Idee von DSMC ist es, statistisches Model Checking zur Bewertung von NNs zu nutzen, die Nichtdeterminismus in Systemen, die als MDPs modelliert sind, auflösen. Die Vielseitigkeit des Ansatzes wird in mehreren Fallbeispielen auf Racetrack gezeigt, einer MDP Benchmark, die zu diesem Zweck entwickelt wurde und die Herausforderung des autonomen Fahrens flexibel modelliert. In einer umfassenden Skalierbarkeitsstudie wird demonstriert, dass DSMC eine leichtgewichtige Technik ist, die die Komplexität der NN-Analyse in Kombination mit dem State Space Explosion Problem bewältigt