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arXiv · 2311.15431

On the piecewise complexity of words and periodic words

M. Praveen·Philippe Schnoebelen·Isa Vialard·Julien Veron
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Abstract

The piecewise complexity $h(u)$ of a word is the minimal length of subwords needed to exactly characterise $u$. Its piecewise minimality index $\rho(u)$ is the smallest length $k$ such that $u$ is minimal among its order-$k$ class $[u]_k$ in Simon's congruence. We study these two measures and provide efficient algorithms for computing $h(u)$ and $\rho(u)$. We also provide efficient algorithms for the case where $u$ is a periodic word, of the form $u=v^n$

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M. Praveen, Philippe Schnoebelen, Isa Vialard, Julien Veron. 2023-11-26. On the piecewise complexity of words and periodic words. https://arxiv.org/abs/2311.15431

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