In this thesis we address problems related to the verification of software-based systems. We aremostly interested in the (safe) design of decision procedures used in verification. In addition, we alsoconsider a modularity problem for a modeling language used in the Why verification platform.Many verification problems can be reduced to a satisfiability problem modulo theories (SMT). In orderto build satisfiability procedures Armando et al. have proposed in 2001 an approach based on rewriting.This approach uses a general calculus for equational reasoning named paramodulation. In general, afair and exhaustive application of the rules of paramodulation calculus (PC) leads to a semi-decisionprocedure that halts on unsatisfiable inputs (the empty clause is then generated) but may diverge onsatisfiable ones. Fortunately, it may also terminate for some theories of interest in verification, and thusit becomes a decision procedure. To reason on the paramodulation calculus, a schematic paramodulationcalculus (SPC) has been studied, notably to automatically prove decidability of single theories and oftheir combinations. The advantage of SPC is that if it halts for one given abstract input, then PC haltsfor all the corresponding concrete inputs. More generally, SPC is an automated tool to check propertiesof PC like termination, stable infiniteness and deduction completeness.A major contribution of this thesis is a prototyping environment for designing and verifying decisionprocedures. This environment, based on the theoretical studies, is the first implementation of theschematic paramodulation calculus. It has been implemented from scratch on the firm basis provided bythe Maude system based on rewriting logic. We show that this prototype is very useful to derive decidabilityand combinability of theories of practical interest in verification. It helps testing new saturationstrategies and experimenting new extensions of the original (schematic) paramodulation calculus.This environment has been applied for the design of a schematic paramodulation calculus dedicated tothe theory of Integer Offsets. This contribution is the first extension of the notion of schematic paramodulationto a built-in theory. This study has led to new automatic proof techniques that are different fromthose performed manually in the literature. The assumptions to apply our proof techniques are easyto satisfy for equational theories with counting operators. We illustrate our theoretical contribution ontheories representing extensions of classical data structures such as lists and records.We have also addressed the problem of modular specification of generic Java classes and methods.We propose extensions to the Krakatoa Modeling Language, a part of the Why platform for provingthat a Java or C program is a correct implementation of some specification. The key features arethe introduction of parametricity both for types and for theories and an instantiation relation betweentheories. The proposed extensions are illustrated on two significant examples: the specification of thegeneric method for sorting arrays and for generic hash map.Both problems considered in this thesis are related to SMT solvers. Firstly, decision procedures areat the core of SMT solvers. Secondly, the Why platform extracts verification conditions from a sourceprogram annotated by specifications, and then transmits them to SMT solvers or proof assistants to checkthe program correctness.
| Identifer | oai:union.ndltd.org:CCSD/oai:tel.archives-ouvertes.fr:tel-01037993 |
| Date | 19 July 2013 |
| Creators | Tushkanova, Elena |
| Publisher | Université de Franche-Comté |
| Source Sets | CCSD theses-EN-ligne, France |
| Language | English |
| Detected Language | English |
| Type | PhD thesis |
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