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Quantitative Static Analysis of Communication Protocols Using Abstract Markov Chains

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Static Analysis (SAS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10422))

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Abstract

In this paper we present a static analysis of communication protocols for inferring parametric bounds of performance metrics. Our analysis is formalized within the theory of abstract interpretation and soundly takes all possible executions into account. We model the concrete executions as Markov chains and we introduce a novel notion of Abstract Markov Chains that provides a finite and symbolic representation to over-approximate the (possibly unbounded) set of concrete behaviors. Our analysis operates in two steps. The first step is a classic abstract interpretation of the source code, using stock numerical abstract domains and a specific automata domain, in order to extract the abstract Markov chain of the program. The second step extracts from this chain particular invariants about the stationary distribution and computes its symbolic bounds using a parametric Fourier-Motzkin elimination algorithm. We present a prototype implementation of the analysis and we discuss some preliminary experiments on a number of communication protocols.

This work is partially supported by the European Research Council under Consolidator Grant Agreement 681393 – MOPSA.

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Notes

  1. 1.

    That being said, this algorithm has shown to be more effective than built-in functions of many off-the-shelf symbolic environments, such as Sage and Mathematica, that did not return solutions for most benchmarks.

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Authors and Affiliations

  1. Sorbonne Universités, UPMC, LIP6, Paris, France

    Abdelraouf Ouadjaout & Antoine Miné

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  1. Abdelraouf Ouadjaout
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  2. Antoine Miné
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Correspondence to Abdelraouf Ouadjaout .

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  1. Dipartimento di Matematica, University of Padova, Padua, Italy

    Francesco Ranzato

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Ouadjaout, A., Miné, A. (2017). Quantitative Static Analysis of Communication Protocols Using Abstract Markov Chains. In: Ranzato, F. (eds) Static Analysis. SAS 2017. Lecture Notes in Computer Science(), vol 10422. Springer, Cham. https://doi.org/10.1007/978-3-319-66706-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-66706-5_14

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