保持LSP性质的无限LSP字和自同态的刻画
Characterization of infinite LSP words and endomorphisms preserving the LSP property
摘要：
对G.在此基础上，我们给出了无限LSP字族的一个$S$ -adic特征，即，一个无限词的家族，它的所有左特殊因子都作为前缀。更精确地说，我们提供了一个有限的态射集$S$和一个自动机${\cal A}$，使得一个无限词是LSP当且仅当它是$S$ -本文首先给出了一个自同态的定义，证明了不存在$S'$集合，并给出了它的一个方向词是${\cal A}$可识别的，然后刻画了保持无限词LSP性质的自同态，从而证明了不存在自同态的集合无限LSP字的集合对应于$S'$ -adic字的集合的自同态。这意味着无论使用哪一组态射，都需要一个自动机。
英文摘要：
Answering a question of G. Fici, we give an $S$-adic characterization of thefamily of infinite LSP words, that is, the family of infinite words having all their left special factors as prefixes.More precisely we provide a finite set of morphisms $S$ and an automaton ${\cal A}$ such that an infinite word is LSP if and only if it is $S$-adic and one of its directive words is recognizable by ${\cal A}$.Then we characterize the endomorphisms that preserve the property of being LSP for infinite words.This allows us to prove that there exists no set $S'$ of endomorphisms for which the set of infinite LSP words corresponds to the set of $S'$-adic words. This implies that an automaton is required no matter which set of morphisms is used.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
