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Periodicity Forcing Words

机译:周期性强迫词

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The Dual Post Correspondence Problem asks, for a given word α, if there exists a non-periodic morphism g and an arbitrary mor-phism h such that g(α) = h(α). Thus α satisfies the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing, and are important to the study of word equations, equality sets and ambiguity of morphisms. In this paper, a 'prime' subset of periodicity forcing words is presented. It is shown that when combined with a particular type of morphism it generates exactly the full set of periodicity forcing words. Furthermore, it is shown that there exist examples of periodicity forcing words which contain any given factor/prefix/suffix. Finally, an alternative class of mechanisms for generating periodicity forcing words is developed, resulting in a class of examples which contrast those known already.
机译:对于给定的单词α,对偶后对应问题问是否存在非周期性的态素g和任意的态素h,使得g(α)= h(α)。因此,当且仅当它属于非平凡的等式集合时,α才满足对偶PCP。不满足对偶PCP的单词称为周期性强制,对于单词方程,等式集和词素歧义的研究非常重要。本文提出了周期性强迫词的“素数”子集。结果表明,当与特定类型的态射结合时,它会精确地生成完整的周期性强迫词集。此外,表明存在一些周期性强制单词的示例,这些单词包含任何给定的因数/前缀/后缀。最终,开发了用于产生周期性强迫词的另一类机制,从而产生了一类示例,这些示例与已知的示例形成对比。

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