arXiv subjects

Jack Romo

Publications and source records attributed to Jack Romo.

3 recordsLinked to original sources

arXiv2025

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology

These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of braided fusion categories (arXiv:2105.15167). They recount the mathematical arguments of the original paper from an expository angle, with background material covering the algebra and homotopy theory required to understand the statement and follow the proof. The notes are aimed at newcomers to the field of (braided) fusion 1- and 2-categories.

math.QA↗

arXiv2021

The Improved GP 2 Compiler

GP 2 is a rule-based programming language based on graph transformation rules which aims to facilitate program analysis and verification. Writing efficient programs in such a language is challenging because graph matching is expensive. GP 2 addresses this problem by providing rooted rules which, under mild conditions, can be matched in constant time. Recently, we implemented a number of changes to Bak's GP 2-to-C compiler in order to speed up graph programs. One key improvement is a new data structure for dynamic arrays called BigArray. This is an array of pointers to arrays of entries, successively doubling in size. To demonstrate the speed-up achievable with the new implementation, we present a reduction program for recognising binary DAGs which previously ran in quadratic time but now runs in linear time when compiled with the new compiler.

cs.PL↗

arXiv2021

Improving the GP 2 Compiler

GP 2 is an experimental programming language based on graph transformation rules which aims to facilitate program analysis and verification. Writing efficient programs in such a language is hard because graph matching is expensive, however GP 2 addresses this problem by providing rooted rules which, under mild conditions, can be matched in constant time using the GP 2 to C compiler. In this report, we document various improvements made to the compiler; most notably the introduction of node lists to improve iteration performance for destructive programs, meaning that binary DAG recognition by reduction need only take linear time where the previous implementation required quadratic time.

cs.PL↗