The equational theory of the Weihrauch lattice with multiplication
CoRR(2024)
Abstract
We study the equational theory of the Weihrauch lattice with multiplication,
meaning the collection of equations between terms built from variables, the
lattice operations ⊔, ⊓, the product ×, 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.
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