Complexity of Grammar Induction for Quantum Types

Most categorical models of meaning use a functor from the syntactic category to the semantic category. When semantic information is available, the problem of grammar induction can therefore be defined as finding preimages of the semantic types under this forgetful functor, lifting the information flow from the semantic level to a valid reduction at the syntactic level. We study the complexity of grammar induction, and show that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete. Our approach could be extended to linguistic type systems such as autonomous or bi-closed categories.Comment: In Proceedings QPL 2014, arXiv:1412.810

Normalization for planar string diagrams and a quadratic equivalence algorithm

In the graphical calculus of planar string diagrams, equality is generated by exchange moves, which swap the heights of adjacent vertices. We show that left- and right-handed exchanges each give strongly normalizing rewrite strategies for connected string diagrams. We use this result to give a linear-time solution to the equivalence problem in the connected case, and a quadratic solution in the general case. We also give a stronger proof of the Joyal-Street coherence theorem, settling Selinger's conjecture on recumbent isotopy

Word problems on string diagrams

String diagrams are graphical representations of morphisms in various sorts of categories. The mathematical results which establish their soundness and completeness provide an elegant bridge between algebra and topology, equating a certain class of topological deformations to the equational theory of an algebraic structure. Beyond this conceptual appeal they also are practical tools to reason in the corresponding categories, making it easy to build intuition about the combinatorics of morphisms and efficiently communicate proofs to peers. Finally, they provide data structures to encode morphisms and manipulate them with computer programs such as proof assistants. Our contributions to the field explore three main directions. First, we define a new class of string diagrams that we call sheet diagrams and prove their soundness and completeness for morphisms in free bimonoidal categories. This makes it possible to use string diagrams in situations involving two monoidal structures, one distributing over the other. Second, the bulk of our work consists in studying how string diagram isotopy can be checked computationally. This is done by providing algorithms or hardness results for a particular class of decision problems, called word problems. Those word problems consist in determining whether two given diagrams can be related via a sequence of isotopy moves, whose nature depends on the algebraic structure at hand. We provide algorithms for the word problems for monoidal categories (or equivalently 2-categories or bicategories) and double categories. We also provide a hardness result for the word problem for braided monoidal categories, showing that this word problem is at least as hard as the unknotting problem, for which no polynomial-time solution is known to date. Finally, we give a taste of how those techniques can be applied to real-world systems. We show how bimonoidal categories model the data transformation workflows offered by OpenRefine, an open source data wrangler focused on tabular data. This model has guided a refactoring of the architecture of the tool and suggests user interfaces to manipulate those workflows

A complete language for faceted dataflow programs

otherInternational audienceWe present a complete categorical axiomatization of a wide class of dataflow programs. This gives a three-dimensional diagrammatic language for workflows, more expressive than the directed acyclic graphs generally used for this purpose. This calls for an implementation of these representations in data transformation tools

Aligned ISNI and Ringgold identifiers for institutions

This dataset provides a correspondence between ISNI and Ringgold identifiers, by combining two datasets: Open ISNI for Institutions, available at http://isni.ringgold.com/ , which provides metadata for institutions identified by ISNI. The dataset of institutions used by ORCID for disambiguation, which also comes from Ringgold, but exposes Ringgold ids. The alignment between the two datasets was performed by exact matching on tuples of (name,city,region,country). This very conservative matching succeeds for about 75% of the 400 000 institutions covered: this high matching rate can be explained by the fact that both datasets come from the same database. Not all Ringgold identifiers are recovered, because ORCID also uses Fundref institutions, and autocompletion can fail for certain names. Structure of the dataset ringgold_metadata_from_orcid.json provides one JSON payload per line, each representing a disambiguated institutition from ORCID, with its Ringgold identifier if provided by ORCID aligned_ringgold_and_isni.tsv provides the aligned dataset, containing all ISNI records and all matching Ringgold records. The Ringgold records that were not matched are not included in this file. License Quoting Ringgold: "The use of the ISNI data contained herein is completely open and you may utilise and share the ISNI identifiers as you see fit." Quoting ORCID: "Per our agreement with Ringgold, we are allowed to share the Ringgold identifiers and limited metadata (organization name, location) under CC0 license, just as the rest of ORCID data are available. We would not be using Ringgold otherwise. If someone gets a Ringgold ID out of ORCID, they are free to use it.