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Path Rewriting in Semistructured Data

We consider in this paper rooted labeled directed graphs as models for semistructured data. A path inclusion constraint, in such graphs, is an expression p <= q where p and q are regular expressions over the alphabet of labels. An path inclusion constraint p <= q is satisfied by a rooted labeled directed graph if the set of nodes reached, from the root, by the words of the language described by p is included in the set of nodes reached, from the root, by the words of the language described by q. We answer here to the following problem : given a set C of path inclusion constraints, given a regular expression p describing an infinite regular language, we want to compute, if it exists, a regular expression f describing a finite language, such that p <= f for every graph satisfying C.