The equational theory of the Weihrauch lattice with multiplication
<|reference_start|>The equational theory of the Weihrauch lattice with multiplication: We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the product $\times$, and the finite parallelization $(-)^*$ which are true however we substitute Weihrauch degrees for the variables. We provide a combinatorial description of these in terms of a reducibility between finite graphs, and moreover, show that deciding which equations are true in this sense is complete for the third level of the polynomial hierarchy.<|reference_end|>
@article{neumann2024the,
    title={The equational theory of the Weihrauch lattice with multiplication},
    author={Eike Neumann, Arno Pauly, C'ecilia Pradic},
    journal={arXiv preprint arXiv:2403.13975},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.13975},
    primaryClass={cs.LO math.LO}
}