Efficient modelling, generation and analysis of Markov automata

Abstract

Quantitative model checking is concerned with the verification of both quantitative and qualitative properties over models incorporating quantitative information. Increases in expressivity of these models allow more types of systems to be analysed, but also raise the difficulty of their efficient analysis. The recently introduced Markov automaton (MA) generalises probabilistic automata and interactive Markov chains, supporting nondeterminism, discrete probabilistic choice as well as stochastic timing. It can be used to compute time-bounded reachability probabilities, expected times and long-run averages. However, an efficient formalism for modelling and generating MAs was still lacking. Additionally, the omnipresent state space explosion always threatens their analysability. This thesis solves the first problem and contributes significantly to the solution of the second. First, we introduce the process-algebraic language MAPA for modelling MAs. It incorporates the use of static as well as dynamic data (such as lists), allowing systems to be modelled efficiently. Second, we introduce five reduction techniques for MAPA specifications. Constant elimination, expression simplification and summation elimination speed up state space generation by simplifying the specification, while dead variable reduction and confluence reduction speed up analysis by reductions in state space size. Since MAs generalise labelled transition systems, discrete-time Markov chains, continuous-time Markov chains, probabilistic automata and interactive Markov chains, our techniques and results are also applicable to all these subclasses. Third, we thoroughly compare confluence reduction to the ample set variant of partial order reduction in the context of probabilistic automata. We show that when preserving branching-time properties, confluence reduction strictly subsumes partial order reduction. Also, we compare the techniques in the practical setting of statistical model checking, demonstrating that the additional potential of confluence indeed may provide larger reductions. We developed the tool SCOOP, containing all our techniques and able to export to the IMCA model checker. Together, these tools for the first time allow the analysis of MAs. Case studies demonstrate the large variety of systems that can be modelled using MAPA. Experiments additionally show significant reductions by all our techniques, sometimes reducing state spaces to less than a percent of their original size: a major step forward in efficient quantitative verification.