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arXiv · 2412.16560

On the piecewise complexity of words

Philippe Schnoebelen·Isa Vialard
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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 initiate a study of these two descriptive complexity measures. Among other results we provide efficient algorithms for computing $h(u)$ and $\rho(u)$ for a given word $u$.

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Philippe Schnoebelen, Isa Vialard. 2024-12-21. On the piecewise complexity of words. https://arxiv.org/abs/2412.16560

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