Rewriting in Varieties of Idempotent Semigroups

Polynomial time multiplication and normal forms in free bands

“…Bands have been widely studied in the literature, some highlights include: the lattice of varieties of bands is completely classified [1,7,9,10] and every such variety is defined by a single identity. Siekmann and Szabó [26] provide an infinite complete rewriting system for every free band; rewriting in further varieties of bands has also been considered in [14]. More recently, combinatorial structures such as hyperplane arrangements, interval greedoids, and matroids have been endowed with the structure of left regular bands (i.e.…”