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| HAL: hal-00369355, version 1 |
| DOI: 10.1007/b87738 |
| Detailed view |  Export this paper |
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| Static Analysis 7th International Symposium, SAS 2000, Santa Barbara, CA : United States (2000) |
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| A Transformational Approach for Generating Non-Linear Invariants |
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| Saddek Bensalem 1Marius Bozga 1 |
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| (2000-06-29) |
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| Computing invariants is the key issue in the analysis of infinite-state systems whether analysis means testing, verification or parameter synthesis. In particular, methods that allow to treat combinations of loops are of interest. We present a set of algorithms and methods that can be applied to characterize over-approximations of the set of reachable states of combinations of self-loops. We present two families of complementary techniques. The first one identifies a number of basic cases of pair of self-loops for which we provide an exact characterization of the reachable states. The second family of techniques is a set of rules based on static analysis that allow to reduce $n$ self-loops ($n\geq 2$) to $n-1$ independent pairs of self-loops. The results of the analysis of the pairs of self-loops can then be combined to provide an over-approximation of the reachable states of the $n$ self-loops. We illustrate our methods by synthesizing conditions under which the Biphase Mark protocol works properly. |
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| 1: | VERIMAG (VERIMAG - IMAG) |
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CNRS : UMR5104 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG) |
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| 2: | Laboratoire Logiciels Systèmes Réseaux (LSR - IMAG) |
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CNRS : UMR5526 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG) |
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| Subject | : | Computer Science/Embedded Systems |
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| invariant generation – acceleration – protocol verification – Presburger arithmetic |
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| hal-00369355, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00369355 | |
| oai:hal.archives-ouvertes.fr:hal-00369355 | |
| From: Marius Bozga | |
| Submitted on: Thursday, 19 March 2009 14:35:39 | |
| Updated on: Thursday, 19 March 2009 14:41:41 | |
