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Preuves par récurrence avec ensembles couvrants contextuels. Application à la vérification de logiciels de télécommunications

Sorin Stratulat 1 
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The software certification process is in most of the cases a
laborious and costly task that needs not only mathematical methods
to express clearly and in a structured manner the software's
expected behavior but also automatic tools to prove some of its
properties. Among the proof techniques, induction is well-suited
to reason on infinite data structures, like integers and lists, or
parameterized systems.

This thesis contains a theoretical and an applicative part. The
first one is centered around the new concept of contextual cover
set (CCS). The principle of induction with CCSs is reflected by an
abstract inference system introducing sufficient conditions for
its sound usage. The modular design of concrete inference rules
is an advantage of this approach. As a case study, we specify the
SPIKE prover as an instance of this system.

In the second part, we first analyze the feature interaction
problem in telecommunications. We propose a methodology for their
detection and resolution by using techniques based on conditional
rewriting and induction. In another application, we obtain the
first formal proof of a generic incremental ABR
conformance algorithm, by using the PVS prover. Then, we
use SPIKE to verify completely automatically the most of the 80
user-defined lemmas.
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Submitted on : Friday, April 12, 2002 - 1:18:28 PM
Last modification on : Friday, February 4, 2022 - 3:34:56 AM
Long-term archiving on: : Friday, April 2, 2010 - 5:57:57 PM


  • HAL Id : tel-00001304, version 1



Sorin Stratulat. Preuves par récurrence avec ensembles couvrants contextuels. Application à la vérification de logiciels de télécommunications. Génie logiciel [cs.SE]. Université Henri Poincaré - Nancy I, 2000. Français. ⟨tel-00001304⟩



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