17,390 research outputs found
Static Analysis of Graph Database Transformations
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
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
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
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 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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