A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910707471089664 |
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| author | Heuberger, Clemens Krenn, Daniel Lipnik, Gabriel F. |
| author_facet | Heuberger, Clemens Krenn, Daniel Lipnik, Gabriel F. |
| contents | In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and $q$-regular sequences (in the sense of Allouche and Shallit) via their linear representations. In particular, we show that the minimisation algorithm for recognisable series can also be used to minimise linear representations of $q$-regular sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_13446 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations Heuberger, Clemens Krenn, Daniel Lipnik, Gabriel F. Combinatorics Formal Languages and Automata Theory 11A63, 68Q45, 68R05, 68R15 In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and $q$-regular sequences (in the sense of Allouche and Shallit) via their linear representations. In particular, we show that the minimisation algorithm for recognisable series can also be used to minimise linear representations of $q$-regular sequences. |
| title | A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations |
| topic | Combinatorics Formal Languages and Automata Theory 11A63, 68Q45, 68R05, 68R15 |
| url | https://arxiv.org/abs/2201.13446 |