This tutorial presents an overview of model checking for both discrete and continuous-time Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three real-world case studies: a probabilistic security protocol, dynamic power management and a biological pathway.

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Stochastic model checking

The ins and outs of the probabilistic model checker MRMC

The Markov Reward Model Checker (MRMC) is a software toolfor verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their rewardextensions. Distinguishing features of MRMC are its support for computing time- and reward-bounded reachability probabilities, (property-driven) bisimulation minimization, and precise on-the-fly steady-state detection. Recent tool features include time-bounded reachability analysis for uniform CTMDPs and CSL model checking by discrete-event simulation. This paper presents the tool's current status and its implementation details.

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The Ins and Outs of the Probabilistic Model Checker MRMC

This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown that this provides a conservative abstraction for both true and false for a three-valued semantics of the branching-time logic CSL (Continuous Stochastic Logic). Experiments on an infinite-state CTMC indicate the feasibility of our abstraction technique.

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Three-valued abstraction for continuous-time Markov chains

MARCIE is a tool for the analysis of generalized stochastic Petri nets which can be augmented by rewards. The supported analysis methods range from qualitative and quantitative standard properties to model checking of established temporal logics. MARCIE's analysis engines for bounded Petri net models are based on Interval Decision Diagrams. They are complemented by simulative and approximative engines to allow for quantitative reasoning on unbounded models. Most of the quantitative analyses benefit from a multi-threaded implementation. This paper gives an overview on MARCIE's functionality and architecture and reports on the recently added feature of CSRL and PLTLc model checking.

MARCIE: model checking and reachability analysis done efficiently

We describe the main features of Smart, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. Smart can combine different formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic state-space generation techniques, as well as symbolic CTL model-checking algorithms, are available. For the study of stochastic and timing behavior, both sparse-storage and Kronecker numerical solution approaches are available when the underlying process is a Markov chain. In addition, discrete-event simulation is always applicable regardless of the stochastic nature of the process, but certain classes of non-Markov models can still be solved numerically. Finally, since Smart targets both the classroom and realistic industrial settings as a learning, research, and application tool, it is written in a modular way that allows for easy integration of new formalisms and solution algorithms.

R. L. Jones

Papers

Logical and Stochastic Modeling with Smart

Logic and stochastic modeling with SMART