自由群的后对应问题的变形
Variations on the Post Correspondence Problem for free groups
摘要：
后对应问题是关于自由幺半群同态的均衡器的一个经典的判定问题。我们证明了这个经典问题的几个变化之间的连接，但在设置的自由群和自由群同态。在其他结果中，并在一定的注入性假设下工作，我们证明了计算一对自由群同态的均衡器的秩可以应用于计算这个均衡器的基础，也可以解决“广义”后对应问题的自由群。
英文摘要：
The Post Correspondence Problem is a classical decision problem about equalisers of free monoid homomorphisms. We prove connections between several variations of this classical problem, but in the setting of free groups and free group homomorphisms. Among other results, and working under certain injectivity assumptions, we prove that computing the rank of the equaliser of a pair of free group homomorphisms can be applied to computing a basis of this equaliser, and also to solve the "generalised" Post Correspondence Problem for free groups.
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