Seminars

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.

Abstract:

We show that equivalence of deterministic top-down tree-to-string transducers is decidable,
thus solving a long standing open problem in formal language theory.
We also present efficient algorithms for subclasses:
polynomial time for total transducers with unary output alphabet (over a given top-down regular domain language),
and co-randomized polynomial time for linear transducers, these results are obtained using techniques from multi-linear algebra.
For our main result, we prove that equivalence can be certified by means of inductive invariants using polynomial ideals.
This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence.