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.

中文翻译：

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并行Hyperedge替换文法

在2018年，事实证明，所有有限生成的虚拟Abelian组都存在多个与上下文无关的单词问题，对于将双曲组的单词问题精确放置在正式语言层次结构中的哪个位置仍然是一个未解决的问题。因此，我们引入了一个新的语言类，即并行超边缘替换字符串语言，其中包含所有多种上下文无关和ET0L语言。我们展示了可以并行化并行超边缘替换语法，这使我们能够建立许多有用的形式语言封闭结果，这些结果与由各种并行超边缘替换语法家族生成的超图和字符串语言有关，从而为将来的工作奠定了基础。区。