  In 2018, it was shown that all finitely generated virtually Abelian groups
have multiple context-free word problems, and it is still an open problem as to
where to precisely place the word problems of hyperbolic groups in the formal
language hierarchy. Motivated by this, we introduce a new language class, the
parallel hyperedge replacement string languages, containing all multiple
context-free and ET0L languages. We show that parallel hyperedge replacement
grammars can be "synchronised", which allows us to establish many useful formal
language closure results relating to both the hypergraph and string languages
generated by various families of parallel hyperedge replacement grammars,
laying the foundations for future work in this area.
