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Amar Hadzihasanovic (Apr 20 2023 at 07:16):I have a new paper on the arXiv, joint work with Diana Kessler.
It will also be presented in the programme of LICS 2023.
Higher-dimensional subdiagram matching
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an (n+1)-cell, which are diagrams of n-cells. We study higher-dimensional diagram rewriting as a mechanism of computation, focussing on the matching problem for rewritable subdiagrams within the combinatorial framework of diagrammatic sets. We provide an algorithm for subdiagram matching in arbitrary dimensions, based on new results on layerings of diagrams, and derive upper bounds on its time complexity. We show that these superpolynomial bounds can be improved to polynomial bounds under certain acyclicity conditions, and that these conditions hold in general for diagrams up to dimension 3. We discuss the challenges that arise in dimension 4.
We also implemented some of the examples in rewalt, in case someone wants to explore them more in detail.