On the piecewise complexity of words
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910759005454336 |
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| author | Schnoebelen, Philippe Vialard, Isa |
| author_facet | Schnoebelen, Philippe Vialard, Isa |
| contents | The piecewise complexity $h(u)$ of a word is the minimal length of subwords needed to exactly characterise $u$. Its piecewise minimality index $ρ(u)$ 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 $ρ(u)$ for a given word $u$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the piecewise complexity of words Schnoebelen, Philippe Vialard, Isa Formal Languages and Automata Theory The piecewise complexity $h(u)$ of a word is the minimal length of subwords needed to exactly characterise $u$. Its piecewise minimality index $ρ(u)$ 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 $ρ(u)$ for a given word $u$. |
| title | On the piecewise complexity of words |
| topic | Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2412.16560 |