MeGARA: Menu-based Game Abstraction and Abstraction Refinement of Markov Automata

Markov automata combine continuous time, probabilistic transitions, and nondeterminism in a single model. They represent an important and powerful way to model a wide range of complex real-life systems. However, such models tend to be large and difficult to handle, making abstraction and abstraction refinement necessary. In this paper we present an abstraction and abstraction refinement technique for Markov automata, based on the game-based and menu-based abstraction of probabilistic automata. First experiments show that a significant reduction in size is possible using abstraction.Comment: In Proceedings QAPL 2014, arXiv:1406.156

Stochastic Bounded Model Checking: Bounded Rewards and Compositionality

We extend the available SAT/SMT-based methods for generating counterexamples of probabilistic systems in two ways: First, we propose bounded rewards, which are appropriate, e. g., to model the energy consumption of autonomous embedded systems, and show how to extend the SMT-based counterexample generation to handle such models. Second, we describe a compositional SAT encoding of the transition relation of Markov models, which exploits the system structure to obtain a more compact formula, which in turn can be solved more efficiently. Preliminary experiments show promising results in both cases

E.: Counterexample generation for Markov chains using SMT-based bounded model checking

Abstract. Generation of counterexamples is a highly important task in the model checking process. In contrast to, e. g., digital circuits where counterexamples typically consist of a single path leading to a critical state of the system, in the probabilistic setting counterexamples may consist of a large number of paths. In order to be able to handle large systems and to use the capabilities of modern SAT-solvers, bounded model checking (BMC) for discrete-time Markov chains was established. In this paper we introduce the usage of SMT-solving over linear real arithmetic for the BMC procedure. SMT-solving, extending SAT with theories in this context on the one hand leads to a convenient way to express conditions on the probability of certain paths and on the other hand allows to handle Markov reward models. We use the former to find paths with high probability first. This leads to more compact counterexamples. We report on some experiments, which show promising results.