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**1 - 3**of**3**### Approximations in Model-Checking and Testing

"... Model Checking and Testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, as an exact verification may be computationally too hard. We present so ..."

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Model Checking and Testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, as an exact verification may be computationally too hard. We present some of notions of approximation with their Logic and Statistics backgrounds, which

### Statistic Analysis for Probabilistic Processes 1 Michel de Rougemont, Mathieu Tracol 2

"... Preprint submitted to Elsevier January 27, 2010Abstract. We associate a statistical vector to a trace and a geometrical embedding to a Markov Decision Process, based on a distance on words, and study basic Membership and Equivalence problems. The Membership problem for a trace w and a Markov Decisio ..."

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Preprint submitted to Elsevier January 27, 2010Abstract. We associate a statistical vector to a trace and a geometrical embedding to a Markov Decision Process, based on a distance on words, and study basic Membership and Equivalence problems. The Membership problem for a trace w and a Markov Decision Process S decides if there exists a strategy on S which generates with high probability traces close to w. We prove that Membership of a trace is testable and Equivalence of MDPs is polynomial time approximable. For Probabilistic Automata, Membership is not testable, and approximate Equivalence is undecidable. We give a class of properties, based on results concerning the structure of the tail σ-field of a finite Markov chain,

### Software Testing with Active Learning in a

"... Abstract. Motivated by Structural Statistical Software Testing (SSST), this paper is interested in sampling the feasible execution paths in the control flow graph of the program being tested. For some complex programs, the fraction of feasible paths becomes tiny, ranging in [10 −10, 10 −5]. When rel ..."

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Abstract. Motivated by Structural Statistical Software Testing (SSST), this paper is interested in sampling the feasible execution paths in the control flow graph of the program being tested. For some complex programs, the fraction of feasible paths becomes tiny, ranging in [10 −10, 10 −5]. When relying on the uniform sampling of the program paths, SSST is thus hindered by the non-Markovian nature of the “feasible path ” concept, due to the long-range dependencies between the program nodes. A divide and generate approach relying on an extended Parikh Map representation is proposed to address this limitation; experimental validation on real-world and artificial problems demonstrates gains of orders of magnitude compared to the state of the art. 1