Raisonnement équationnel et méthodes de combinaison: de la programmation à la preuve

Christophe Ringeissen 1
1 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this document, we present decision procedures and solvers which are useful in verification. We consider first order logic with equality. This logic is undecidable in general, but the study of interesting fragments leads to automatic (push-button) tools. The notion of equality is particularly interesting for programming via oriented equalities (rule-based programming) or for deriving proofs thanks to the principle of replacement of equal by equal. In a modelisation using first order logic with equality, we easily have to deal with a problem involving different theories. For instance, these theories may be used to modelise the functions, the arithmetic operations and the memory of a program. Hence, we have to face a problem expressed in a combination of theories, which is interesting to solve in a modular way by using the decision procedures known for individual theories. This problem is the bulk of my research interests. The originality of my approach consists in developing combination methods which are useful in the domain of verification. All the given decision procedures are designed by using a rule-based formalism to ease their proofs.
Document type :
Habilitation à diriger des recherches
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00578600
Contributor : Christophe Ringeissen <>
Submitted on : Monday, March 21, 2011 - 4:11:27 PM
Last modification on : Friday, May 17, 2019 - 11:37:57 AM
Long-term archiving on : Thursday, November 8, 2012 - 12:16:13 PM

Identifiers

  • HAL Id : tel-00578600, version 1

Citation

Christophe Ringeissen. Raisonnement équationnel et méthodes de combinaison: de la programmation à la preuve. Génie logiciel [cs.SE]. Université Henri Poincaré - Nancy I, 2009. ⟨tel-00578600⟩

Share

Metrics

Record views

520

Files downloads

248