Overall Objectives
Research Program
Application Domains
Software and Platforms
New Results
Partnerships and Cooperations
Inria | Raweb 2013 | Exploratory Action
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Section: New Results

Automated Theorem Proving

Mélanie Jacquel (Siemens) and David Delahaye developed Super Zenon [5] , a generalization of the extension of Zenon to superdeduction to handle any first order theory. To do so, they designed heuristics able to automatically transform axioms of a theory into rewrite rules. This new tool has been tested over the first order problems of the TPTP library and a significant increase has been observed. A first distribution of this tool (under GPL licence) is planned in the first months of 2014. In addition, an integration to the Rodin platform is also planned with the help of Laurent Voisin (Systerel). This integration should allow us to apply this tool in the context of Event-B.

Pierre Halmagrand, David Delahaye, Damien Doligez, and Olivier Hermant developed Zenon Modulo [22] , [23] , an extension of Zenon to Deduction modulo. Like Super Zenon, this new tool is able to deal with any first order theory and relies on an heuristic able to automatically transform axioms of a theory into rewrite rules. This tool has also been tested over the first order problems of the TPTP library and a similar increase of performance (compared to Super Zenon) has been observed. Frédéric Gilbert has developed a Dedukti backend for this extension, which is based on a double-negation transformation that allows us to transform classical proofs produced by Zenon Modulo into intuitionistic proofs in Dedukti. This tool is intended to be applied in the framework of the BWare project in order to automatically verify proof obligations coming from the modeling of industrial applications. To do so, the idea is to manually transform the B set theory into a theory modulo and provide it to Zenon Modulo in order to verify the proof obligations of the BWare project.

Guillaume Burel and Simon Cruanes have designed a method to scan sets of first-order clauses in order to detect the presence of instances of axiomatic theories (group structures, total orderings, etc.), even during a saturation process (so that theories that only become apparent during the proof search can be detected) [21] . To this end, they introduced the concept of meta-prover, a Datalog system that reasons over properties of the problem, and communicates with the saturation prover. This technique made some applications possible, such as the use of generic lemma and an equational redundancy criterion for some theories, and was implemented in Zipperposition.

Simon Cruanes has been working on superposition modulo linear arithmetic, using Zipperposition as a test bed. The focus is on problems with rational or integer arithmetic mixed with first-order reasoning, an area in which SMT solvers struggle. The work is still preliminary, but shows promising results.

Depending on the logic for finite structures, which is defined by Gilles Dowek and Ying Jiang (Beijing), Kailiang Ji has extended the use of proof search algorithms in Deduction modulo to automatically prove some graph properties, such as (un)reachability, which can be described by CTL formulas. A technical report about this has been given on Locali 2013 in Beijing.

Together with Tayssir Touili (University Paris Diderot) Hugo Macedo has shown how to advance the performance of the application of model checking techniques in the domain of malicious software detection. The work consisted in leveraging the reachability analysis used in the model checking of pushdown systems to infer malicious behavior patterns from known malware. From such new application a malware detection tool was prototyped and put to the test with instances of “in the wild” (real world) malicious software. This work was published in a large security venue and the details about the technique follow in [29] .

Kim-Quyen Ly extended her formally-proved (in Coq ) automated termination-certificate (for first-order rewrite systems) verifier Rainbow for dealing with certificates using arguments filtering [39] and other termination techniques.