Approximation and Semantic Tree-width of Conjunctive Regular Path Queries
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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 for the restricted but practically relevant case where all regular expressions of the query are of the form a^* or (a_1 + … + a_n) we show that the complexity of the problem drops to Π_2^p. 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'.
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