L'objectiu del grup és la producció de contribucions rellevants en les àrees d'expertesa dels components del grup i la seva disseminació en revistes i conferències internacionals de prestigi reconegut. És voluntat del grup que les contribucions tinguin un impacte significatiu a llarg termini. La transferència de tecnologia és considerada com una conseqüència de l'excel·lència en la recerca i s'ha de portar a terme com un mitjà per incrementar l'impacte dels resultats, obtenir recursos per al grup i explorar nous temes per a la recerca en el futur.
We define a new class of tree automata with constraints and prove decidability of the emptiness problem for this class in exponential time. As a consequence, we obtain several EXPTIME-completeness results for problems on images of regular tree languages under tree homomorphisms, like set inclusion, regularity (HOM problem), and finiteness of set difference. Our result also has implications in term rewriting, since the set of reducible terms of a term rewrite system can be described as the image of a tree homomorphism. In particular, we prove that inclusion of sets of normal forms of term rewrite systems can be decided in exponential time. Analogous consequences arise in the context of XML typechecking, since types are defined by tree automata and some type transformations are homomorphic.
Relational joins are at the core of relational algebra, which in turn is the core of the standard database query language SQL. As their evaluation is expensive and very often dominated by the output size, it is an important task for database query optimizers to compute estimates on the size of joins and to find good execution plans for sequences of joins. We study these problems from a theoretical perspective, both in the worst-case model and in an average-case model where the database is chosen according to a known probability distribution. In the former case, our first key observation is that the worst-case size of a query is characterized by the fractional edge cover number of its underlying hypergraph, a combinatorial parameter previously known to provide an upper bound. We complete the picture by proving a matching lower bound and by showing that there exist queries for which the join-project plan suggested by the fractional edge cover approach may be substantially better than any join plan that does not use intermediate projections. On the other hand, we show that in the average-case model, every join-project plan can be turned into a plan containing no projections in such a way that the expected time to evaluate the plan increases only by a constant factor independent of the size of the database. Not surprisingly, the key combinatorial parameter in this context is the maximum density of the underlying hypergraph. We show how to make effective use of this parameter to eliminate the projections.