具有多元上下文无关字问题的群体
Groups with poly-context-free word problem
摘要：
我们考虑一类群体的字问题是多上下文无关的，也就是说，一个交叉的许多上下文无关的语言。我们证明了任何群，它实际上是一个自由群的直积的一个可生成的子群有poly-context-free字问题，并猜想，反过来也成立。我们证明了我们的猜想几类可溶性群体，包括亚阿贝尔群和扭自由可溶性群体，目前的进展解决一般可溶性群体的猜想。一些用于证明语言不是多上下文无关的技术可能是独立的兴趣。
英文摘要：
We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free groups has poly-context-free word problem, and conjecture that the converse also holds. We prove our conjecture for several classes of soluble groups, including metabelian groups and torsion-free soluble groups, and present progress towards resolving the conjecture for soluble groups in general. Some of the techniques introduced for proving languages not to be poly-context-free may be of independent interest.
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