Polynomial-Time Program Equivalence for Machine Knitting
| Nathan Hurtig | Jenny Han Lin | Thomas S. Price | Adriana Schulz | James McCann | Gilbert Louis Bernstein |
Proc. ACM Program. Lang. (2025)
We present an algorithm that canonicalizes the algebraic representations of the topological semantics of machine knitting programs. Machine knitting is a staple technology of modern textile production where hundreds of mechanical needles are manipulated to form yarn into interlocking loop structures. Our semantics are defined using a variant of a monoidal category, and they closely correspond to string diagrams. We formulate our canonicalization as an Abstract Rewriting System (ARS) over words in our category, and prove that our algorithm is correct and runs in polynomial time.
Nathan Hurtig, Jenny Han Lin, Thomas S. Price, Adriana Schulz, James McCann, Gilbert Louis Bernstein (2025). Polynomial-Time Program Equivalence for Machine Knitting. Proc. ACM Program. Lang., 9(ICFP).
@article{10.1145/3747517,
author = {Nathan Hurtig and Jenny Han Lin and Thomas S. Price and Adriana Schulz and James McCann and Gilbert Louis Bernstein},
title = {Polynomial-Time Program Equivalence for Machine Knitting},
year = {2025},
issue_date = {August 2025},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {9},
number = {ICFP},
url = {https://doi.org/10.1145/3747517},
doi = {10.1145/3747517},
journal = {Proc. ACM Program. Lang.},
month = aug,
articleno = {248},
numpages = {29},
keywords = {braids, canonicalization, fenced tangles, machine knitting, monoidal categories, normal forms, program equivalence, string diagrams}
}
