We present a normalisation framework for linguistic representations and illustrate its use by normalising the Stanford Dependency graphs (SDs) produced by the Stanford parser into Labelled Stanford Dependency graphs (LSDs). The normalised representations are evaluated both on a testsuite of constructed examples and on free text. The resulting representations improve on standard Predicate/Argume...

In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these algorithms must either be mechanically verified or their results verifiable by independent checkers. We analyze a state-of-the-art algorithm for (described McKay Piperno) formulate it terms formal proof system. provide an implementation that can export the obtained graph is form given ...

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The 1-2-3 Conjecture states that every connected graph different from K2 admits a proper 3-(edge-)labelling, i.e., can have its edges labelled with 1,2,3 so no two adjacent vertices are incident to the same sum of labels. In connection some recent optimisation variants this conjecture, in paper we investigate role label 3 3-labellings graphs. An intuition previous investigations is that, genera...

Dujmović et al. [J. ACM '20] proved that every planar graph is isomorphic to a subgraph of the strong product bounded treewidth and path. Analogous results were obtained for graphs Euler genus or apex-minor-free graphs. These tools have been used solve longstanding problems on queue layouts, non-repetitive colouring, p-centered adjacency labelling. This paper proves analogous structure theorems...

We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds. Previously in [Br3] similar results were established for some domains on coverings of St...

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In this paper we answer an important question posed in the paper [GHS] by Gromov, Henkin and Shubin on existence of sufficiently many holomorphic L2 functions on arbitrary coverings of strongly pseudoconvex manifolds.