  This paper studies complete rewriting systems and biautomaticity for three
interesting classes of finite-rank homogeneous monoids: Chinese monoids,
hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give
new presentations via finite complete rewriting systems, using more lucid
constructions and proofs than those given independently by Chen & Qui and
G\"uzel Karpuz; we then construct biautomatic structures. For hypoplactic
monoids, we construct finite complete rewriting systems and biautomatic
structures. For sylvester monoids, which are not finitely presented, we prove
that the standard presentation is an infinite complete rewriting system, and
construct biautomatic structures. Consequently, the monoid algebras
corresponding to monoids of these classes are automaton algebras in the sense
of Ufnarovskij.
