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**1 - 5**of**5**### On Abstraction of Probabilistic Systems

"... Abstract. Probabilistic model checking extends traditional model check-ing by incorporating quantitative information about the probability of system transitions. However, probabilistic models that describe inter-esting behavior are often too complex for straightforward analysis. Ab-straction is one ..."

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Abstract. Probabilistic model checking extends traditional model check-ing by incorporating quantitative information about the probability of system transitions. However, probabilistic models that describe inter-esting behavior are often too complex for straightforward analysis. Ab-straction is one way to deal with this complexity: instead of analyzing the (“concrete”) model, a simpler (“abstract”) model that preserves the relevant properties is built and analyzed. This paper surveys various ab-straction techniques proposed in the past decade. For each abstraction technique we identify in what sense properties are preserved or provide alternatively suitable boundaries. 1

### Diagnosis of Probabilistic Models using Causality and Regression

"... The counterexample in probabilistic model checking (PMC) is a set of paths in which a path formula holds, and their accumulated probability violates the probability bound. However, understanding the counterexample is not an easy task. In this paper we address the complementary task of counterexample ..."

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The counterexample in probabilistic model checking (PMC) is a set of paths in which a path formula holds, and their accumulated probability violates the probability bound. However, understanding the counterexample is not an easy task. In this paper we address the complementary task of counterexample generation, which is the counterexample analysis. We propose an aided-diagnostic method for probabilistic counterexamples based on the notions of causality and regression analysis. Given a counterexample for a Probabilistic CTL (PCTL)/Continuous Stochastic Logic (CSL) formula that does not hold over Discrete Time Markov Chain (DTMC)/Continuous Time Markov Logic (CTMC) model, this method generates the causes of the violation, and describes their contribution to the error in the form of a regression model.

### Contractual Date of Delivery to the CEC: 30-Sep-2013 Actual Date of Delivery to the CEC: 30-Sep-2013 Organisation name of lead contractor for this deliverable: UNC

, 2013

"... 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 u ..."

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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 well-understandable counterexample. Note: “This deliverable is based on material that has been published in QEST 2013,

### Leveraging Weighted Automata in Compositional Reasoning about Concurrent Probabilistic Systems

"... We propose the first sound and complete learning-based com-positional verification technique for probabilistic safety proper-ties on concurrent systems where each component is an Markov decision process. Different from previous works, weighted as-sumptions are introduced to attain completeness of ou ..."

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We propose the first sound and complete learning-based com-positional verification technique for probabilistic safety proper-ties on concurrent systems where each component is an Markov decision process. Different from previous works, weighted as-sumptions are introduced to attain completeness of our frame-work. Since weighted assumptions can be implicitly represented by multi-terminal binary decision diagrams (MTBDD’s), we give an L∗-based learning algorithm for MTBDD’s to infer weighted assumptions. Experimental results suggest promising outlooks for our compositional technique.

### HIGH-LEVEL COUNTEREXAMPLES FOR PROBABILISTIC AUTOMATA

, 2014

"... Vol. 11(1:15)2015, pp. 1–23 www.lmcs-online.org ..."

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