Seminars

Counter-Example-Guided Abstraction Refinement (CEGAR) has been very successful in model checking.
Since then, it has been applied to many different problems. It is especially proved to be a highly successful practical approach for solving the PSPACE complete QBF problem. In this paper, we propose a new CEGAR-like approach for tackling PSPACE complete problems that we call RECAR (Recursive Explore and Check Abstraction Refinement). We show that this generic approach is sound and complete. Then we propose a specific implementation of the RECAR approach to solve the modal logic K satisfiability problem. We implemented both CEGAR and RECAR approaches for the modal logic K satisfiability problem within the solver MoSaiC. We compared experimentally those approaches to the state-of-the-art solvers for that problem. The RECAR approach outperforms the CEGAR one for that problem and also compares favorably against the state-of-the-art on the benchmarks considered.

In database management, one of the principal task is to optimize the queries to evaluate them efficiently. It is in particular the case for recursive queries for which their evaluation can lead to crawl all the database. In particular, one of the main question is to minimize the queries in order to avoid to evaluate useless parts of the query. The core theoretical question around this line of work is the problem of inclusion of a query in another. Interestedly, this question is related to an important question in IA which is to answer a query when the data is incomplete but rules are given to derive new information. This problem is called certain query answering. In both context, if both problem are undecidable in general, there are fragments based on guardedness that are decidable due to the fact there exists witness of the problems that have a bounded tree width and that their encoding in trees is regular. Furthermore, the queries can be translated in MSO. In both contexts, Courcelle’s Theorems imply the decidability of both problems. I will present to the different results on the translation of logic class of formula for our problems into tree automata to obtain tight bounds to the problems of inclusion of recursive queries or certain query answering.