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—Model checkers for concurrent probabilistic systems have become very popular within the last decade. The study of long-run average behavior has however received only scant attention in this area, at least from the implementation perspective. This paper studies the problem of how to efficiently realize an algorithm for computing optimal long-run average(More)
We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the(More)
— This paper reports on our efforts to link an industrial state-of-the-art modelling tool to academic state-of-the-art analysis algorithms. In a nutshell, we enable timed reachability analysis of uniform continuous-time Markov decision processes, which are generated from STATEMATE models. We give a detailed explanation of several construction,(More)
Since its introduction in 1999, bounded model checking has gained industrial relevance for detecting errors in digital and hybrid systems. One of the main reasons for this is that it always provides a counterexample when an erroneous execution trace is found. Such a counterexample can guide the designer while debugging the system. In this paper we are(More)
Branch & Cut is today's state-of-the-art method to solve 0/1-integer linear programs. Important for the success of this method is the generation of strong valid inequalities, which tighten the linear programming relaxation of 0/1-IPs and thus allow for early pruning of parts of the search tree. In this paper we present a novel approach to generate valid(More)
We propose a new approach to compute counterexamples for violated ω-regular properties of discrete-time Markov chains and Markov decision processes. Whereas most approaches compute a set of system paths as a counterexample, we determine a critical subsystem that already violates the given property. In earlier work we introduced methods to compute such(More)
This paper introduces a novel counterexample generation approach for the verification of discrete-time Markov chains (DTMCs) with two main advantages: (1) We generate abstract counterexamples which can be refined in a hierarchical manner. (2) We aim at minimizing the number of states involved in the counterexamples, and compute a critical subsystem of the(More)
—Discrete-Time Markov Chains (DTMCs) are a widely-used formalism to model probabilistic systems. On the one hand, available tools like PRISM or MRMC offer efficient model checking algorithms and thus support the verification of DTMCs. However, these algorithms do not provide any diagnostic information in the form of counterexamples, which are highly(More)
We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key ingredients: a graph decomposition into strongly connected subgraphs combined with a novel factorization strategy for polynomials.(More)