Path constraints in semistructured data

Abstract

We consider semistructured data as multirooted edge-labelled directed graphs, and path inclusion constraints on these graphs. A path inclusion constraint p ⪯ q is satisfied by a semistructured data if any node reached by the regular query p is also reached by the regular query q . In this paper, two problems are mainly studied: the implication problem and the problem of the existence of a finite exact model. – We give a new decision algorithm for the implication problem of a constraint p ⪯ q by a set of bounded path constraints p i ⪯ u i where p , q , and the p i ’s are regular path expressions and the u i ’s are words, improving in this particular case, the more general algorithms of S. Abiteboul and V. Vianu, and N. Alechina et al. In the case of a set of word equalities u i ≡ v i , we provide a more efficient decision algorithm for the implication of a word equality u ≡ v , improving the more general algorithm of P. Buneman et al. We prove that, in this case, implication for nondeterministic models is equivalent to implication for (complete) deterministic ones. – We introduce the notion of exact model: an exact model of a set of path constraints C satisfies the constraint p ⪯ q if and only if this constraint is implied by C . We prove that any set of constraints has an exact model and we give a decidable characterization of data which are exact models of bounded path inclusion constraints sets.