[M2F] Rémi Morvan

** Approximation and Semantic Tree-width of Conjunctive Regular Path Queries **

We show that the problem of whether a query is equivalent to a query of tree-width k is decidable, for the class of Unions of Conjunctive Regular Path Queries with two-way navigation (UC2RPQs). A previous result by Barceló, Romero, and Vardi has shown decidability for the case k=1, and here we show that decidability in fact holds for any arbitrary k>1. The algorithm is in 2ExpSpace, but we show that the complexity drops to the second level of the polynomial hierarchy for a restricted but practically relevant case of queries obtained by only allowing simple regular expressions.
We also investigate the related problem of approximating a UC2RPQ by queries of small tree-width. We exhibit an algorithm which, for any fixed number k, builds the maximal under-approximation of tree-width k of a UC2RPQ. The maximal under-approximation of tree-width k of a query q is a query q' of tree-width k which is contained in q in a maximal and unique way, that is, such that for every query q'' of tree-width k, if q'' is contained in q then q'' is also contained in q'. Joint work with Diego Figueira.