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24
On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime 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 ..."
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Cited by 107 (25 self)
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Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime 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 realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
Minimal critical subsystems for discretetime Markov models
 IN: PROC. OF TACAS. VOL. 7214 OF LNCS
, 2012
"... We propose a new approach to compute counterexamples for violated ωregular properties of discretetime 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. ..."
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Cited by 13 (6 self)
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We propose a new approach to compute counterexamples for violated ωregular properties of discretetime 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 subsystems based on a search for shortest paths. In this paper we use SMT solvers and mixed integer linear programming to determine minimal critical subsystems.
From probabilistic counterexamples via causality to fault trees
, 2011
"... Abstract. In recent years, several approaches to generate probabilistic counterexamples have been proposed. The interpretation of stochastic counterexamples, however, continues to be problematic since they have to be represented as sets of paths, and the number of paths in this set may be very large ..."
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Cited by 11 (9 self)
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Abstract. In recent years, several approaches to generate probabilistic counterexamples have been proposed. The interpretation of stochastic counterexamples, however, continues to be problematic since they have to be represented as sets of paths, and the number of paths in this set may be very large. Fault trees (FTs) are a wellestablished industrial technique to represent causalities for possible system hazards resulting from system or system component failures. In this paper we suggest a method to automatically derive FTs from counterexamples, including a mapping of the probability information onto the FT. We extend the structural equation approach by Pearl and Halpern, which is based on Lewis counterfactuals, so that it serves as a justification for the causality that our proposed FT derivation rules imply. We demonstrate the usefulness of our approach by applying it to an industrial case study. 1
Dipro  a tool for probabilistic counterexample generation
 in Model Checking Software  Pro. of the 18th Int. SPIN Workshop (SPIN 2011), ser. LNCS
, 2011
"... Abstract. The computation of counterexamples for probabilistic model checking has been an area of active research over the past years. In spite of the achieved theoretical results in this field, there is no freely available tool that allows for the computation and representation of probabilistic cou ..."
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Cited by 8 (5 self)
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Abstract. The computation of counterexamples for probabilistic model checking has been an area of active research over the past years. In spite of the achieved theoretical results in this field, there is no freely available tool that allows for the computation and representation of probabilistic counterexamples. We present an open source tool called DiPro that can be used with the PRISM and MRMC probabilistic model checkers. It allows for the computation of probabilistic counterexamples for discrete time Markov chains (DTMCs), continuous time Markov chains (CTMCs) and Markov decision processes (MDPs). The computed counterexamples can be rendered graphically. 1
K∗: A heuristic search algorithm for finding the k shortest paths
, 2011
"... We present a directed search algorithm, called K ∗ , for finding the k shortest paths between a designated pair of vertices in a given directed weighted graph. K ∗ has two advantages compared to current kshortestpaths algorithms. First, K ∗ operates onthefly, which means that it does not require ..."
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Cited by 7 (1 self)
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We present a directed search algorithm, called K ∗ , for finding the k shortest paths between a designated pair of vertices in a given directed weighted graph. K ∗ has two advantages compared to current kshortestpaths algorithms. First, K ∗ operates onthefly, which means that it does not require the graph to be explicitly available and stored in main memory. Portions of the graph will be generated as needed. Second, K ∗ can be guided using heuristic functions. We prove the correctness of K ∗ and determine its asymptotic worstcase complexity when using a consistent heuristic to be the same as the state of the art, O(m + n log n + k), with respect to both runtime and space, where n is the number of vertices and m is the number of edges of the graph. We present an experimental evaluation of K ∗ by applying it to route planning problems as well as counterexample generation for stochastic model checking. The experimental results illustrate that due to the use of heuristic, onthefly search K ∗ can use less time and memory compared to the most efficient kshortestpaths algorithms known so far.
Highlevel Counterexamples for Probabilistic Automata
"... Abstract. Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system’s states, both of which are of ..."
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Cited by 5 (1 self)
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Abstract. Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system’s states, both of which are of limited use in manual debugging. Many probabilistic systems are described in a guarded command language like the one used by the popular model checker PRISM. In this paper we describe how a minimal subset of the commands can be identified which together already make the system erroneous. We additionally show how the selected commands can be further simplified to obtain a wellunderstandable counterexample. 1
Directed and heuristic counterexample generation for probabilistic model checking: a comparative evaluation
 In QUOVADIS ‘10: Proceedings of the 2010 ICSE Workshop on Quantitative Stochastic Models in the Verification and Design of Software Systems
, 2010
"... The generation of counterexamples for probabilistic model checking has been an area of active research over the past five years. Tangible outcome of this research are novel directed and heuristic algorithms for efficient generation of probabilistic counterexamples, such as K ∗ and XBF. In this paper ..."
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Cited by 3 (3 self)
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The generation of counterexamples for probabilistic model checking has been an area of active research over the past five years. Tangible outcome of this research are novel directed and heuristic algorithms for efficient generation of probabilistic counterexamples, such as K ∗ and XBF. In this paper we present an empirical evaluation of the efficiency of these algorithms and the wellknown Eppstein’s algorithm. We will also evaluate the effect of optimisations applied to Eppstein, K ∗ and XBF. Additionally, we will show, how information produced during model checking can be used to guide the search for counterexamples. This is a first step towards automatically generating heuristic functions. The experimental evaluation of the various algorithms is done by applying them to one case study, knwon from the literature on probabilistic model checking and one case study taken from the automotive industry.
Symbolic Counterexample Generation for Discretetime Markov Chains
"... In this paper we investigate the generation of counterexamples for discretetime Markov chains (DTMCs) and PCTL properties. Whereas most available methods use explicit representations for at least some intermediate results, our aim is to develop fully symbolic algorithms. As in most related work, ou ..."
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Cited by 3 (0 self)
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In this paper we investigate the generation of counterexamples for discretetime Markov chains (DTMCs) and PCTL properties. Whereas most available methods use explicit representations for at least some intermediate results, our aim is to develop fully symbolic algorithms. As in most related work, our counterexample computations are based on path search. We first adapt bounded model checking as a path search algorithm and extend it with a novel SATsolving heuristics to prefer paths with higher probabilities. As a second approach, we use symbolic graph algorithms to find counterexamples. Experiments show that our approaches, in contrast to other existing techniques, are applicable to very large systems with millions of states.
On the Synergy of Probabilistic Causality Computation and Causality Checking
"... Abstract. In recent work on the safety analysis of systems we have shown how causal relationships amongst events can be algorithmically inferred from probabilistic counterexamples and subsequently be mapped to fault trees. The resulting fault trees were significantly smaller and hence easier to unde ..."
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Cited by 3 (3 self)
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Abstract. In recent work on the safety analysis of systems we have shown how causal relationships amongst events can be algorithmically inferred from probabilistic counterexamples and subsequently be mapped to fault trees. The resulting fault trees were significantly smaller and hence easier to understand than the corresponding probabilistic counterexample, but still contain all information needed to discern the causes for the occurrence of a hazard. More recently we have developed an approach called Causality Checking which is integrated into the statespace exploration algorithms used for qualitative model checking and which is capable of computing causality relationships onthefly. The causality checking approach outperforms the probabilistic causality computation in terms of runtime and memory consumption, but can not provide a probabilistic measure. In this paper we combine the strengths of both approaches and propose an approach where the causal events are computed using causality checking and the probability computation can be limited to the causal events. We demonstrate the increase in performance of our approach using several case studies. 1
K∗: Heuristicsguided, onthefly k shortest paths search
, 2010
"... We present a search algorithm, called K∗, for finding the k shortest paths (KSP) between a designated pair of vertices in a given directed weighted graph. As a directed algorithm, K ∗ has two advantages compared to current KSP algorithms. First, K ∗ performs onthefly, which means that it does no ..."
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Cited by 2 (2 self)
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We present a search algorithm, called K∗, for finding the k shortest paths (KSP) between a designated pair of vertices in a given directed weighted graph. As a directed algorithm, K ∗ has two advantages compared to current KSP algorithms. First, K ∗ performs onthefly, which means that it does not require the graph to be explicitly available and stored in main memory. Portions of the graph will be generated as needed. Second, K ∗ can be guided using heuristic functions. We discuss the properties of K∗, including its correctness, and its asymptotic worstcase complexity, which has been shown to be ofO(m+n logn+ k) with respect to both runtime and space, where n is the number of vertices andm is the number of edges of the graph. We report on experimental results which illustrate the favorable performance of K ∗ compared to the most efficient kshortestpaths algorithms known so far. In other work it has been shown that K ∗ can be used to efficiently compute counterexamples for stochastic model checking.