A marked free monoid morphism is a morphism for which the image of each generator starts with a different letter, and immersions are the analogous maps in free groups. We show that the (simultaneous) PCP is decidable for immersions of free groups, and provide an algorithm to compute bases for the sets, called equalisers, on which the immersions take the same values. We also answer a question of Stallings about the rank of the equaliser. Analogous results are proven for marked morphisms of free monoids.

中文翻译：

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某些自由群和幺半群态射的后对应问题和均衡器

标记自由幺半群态射是每个生成器的图像以不同字母开头的态射，浸入是自由群中的类似映射。我们表明（同时）PCP 可判定自由组的浸入，并提供一种算法来计算集合的基数，称为均衡器，浸入量采用相同的值。我们还回答了 Stallings 关于均衡器排名的问题。对于自由幺半群的显着态射证明了类似的结果。