17,390 research outputs found

    Static Analysis of Graph Database Transformations

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    We investigate graph transformations, defined using Datalog-like rules based on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we study two fundamental static analysis problems: type checking and equivalence of transformations in the presence of graph schemas. Additionally, we investigate the problem of target schema elicitation, which aims to construct a schema that closely captures all outputs of a transformation over graphs conforming to the input schema. We show all these problems are in EXPTIME by reducing them to C2RPQ containment modulo schema; we also provide matching lower bounds. We use cycle reversing to reduce query containment to the problem of unrestricted (finite or infinite) satisfiability of C2RPQs modulo a theory expressed in a description logic

    The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks

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    We show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a holomorphic-disk analog of Hitchin's mini-twistor correspondence.Comment: 11 pages, LaTeX2e. Revised version strengthens result and completes proo

    Unoriented 3d TFTs

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    This paper generalizes two facts about oriented 3d TFTs to the unoriented case. On one hand, it is known that oriented 3d TFTs having a topological boundary condition admit a state-sum construction known as the Turaev-Viro construction. This is related to the string-net construction of fermionic phases of matter. We show how Turaev-Viro construction can be generalized to unoriented 3d TFTs. On the other hand, it is known that the "fermionic" versions of oriented TFTs, known as Spin-TFTs, can be constructed in terms of "shadow" TFTs which are ordinary oriented TFTs with an anomalous Z2\mathbb{Z}_2 1-form symmetry. We generalize this correspondence to Pin+^+-TFTs by showing that they can be constructed in terms of ordinary unoriented TFTs with anomalous Z2\mathbb{Z}_2 1-form symmetry having a mixed anomaly with time-reversal symmetry. The corresponding Pin+^+-TFT does not have any anomaly for time-reversal symmetry however and hence it can be unambiguously defined on a non-orientable manifold. In case a Pin+^+-TFT admits a topological boundary condition, one can combine the above two statements to obtain a Turaev-Viro-like construction of Pin+^+-TFTs. As an application of these ideas, we construct a large class of Pin+^+-SPT phases.Comment: 41 pages, 31 figures, v2: additional references, v3: minor revisio
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