Boundedness of Conjunctive Regular Path Queries We study the boundedness problem for unions of conjunctive regular path queries with inverses (UC2RPQs). This is the problem of, given a UC2RPQ, checking whether it is equivalent to a union of conjunctive queries (UCQ). We show the problem to be ExpSpacecomplete, thus coinciding with the complexity of containment for UC2RPQs. As a corollary, when a UC2RPQ is bounded, it is equivalent to a UCQ of at most tripleexponential size, and in fact we show that this bound is optimal. We also study better behaved classes of UC2RPQs, namely acyclic UC2RPQs of bounded thickness, and strongly connected UCRPQs, whose boundedness problem are, respectively, PSpacecomplete and Pip_2complete. Most upper bounds exploit results on limitedness for distance automata, in particular extending the model with alternation and twowayness, which may be of independent interest.

Revisiting Graph Width Measures for CNFEncodings We consider bounded width CNFformulas where the width is measured by popular graph width measures on graphs associated to CNFformulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied for their uses in the design of algorithms for various computational problems on CNFformulas. Here we consider the expressivity of these formulas in the model of clausal encodings with auxiliary variables. We first show that bounding the width for many of the measures from the literature leads to a dramatic loss of expressivity, restricting the formulas to such of low communication complexity. We then show that the width of optimal encodings with respect to different measures is strongly linked: there are two classes of width measures, one containing primal treewidth and the other incidence cliquewidth, such that in each class the width of optimal encodings only differs by constant factors. Moreover, between the two classes the width differs at most by a factor logarithmic in the number of variables. Both these results are in stark contrast to the setting without auxiliary variables where all width measures we consider here differ by more than constant factors and in many cases even by linear factors.