2024/03/20 by Eike Neumann, Neumann, Eike, Arno Pauly +3
Computer Science · Engineering · #03D30 #08A50 #68Q17 #Advanced Algebra and Logic #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2403.13975
openalex publication_date 2024/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ×, 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.