Complexity of Linear Subsequences of $k$-Automatic Sequences
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908932307419136 |
|---|---|
| author | Moradi, Delaram Rampersad, Narad Shallit, Jeffrey |
| author_facet | Moradi, Delaram Rampersad, Narad Shallit, Jeffrey |
| contents | We construct automata with input(s) in base $k$ recognizing some basic relations and study their number of states. We also consider some basic operations on $k$-automatic sequences $(h(i))_{i \geq 0}$ and discuss their state complexity. We find a relationship between subword complexity of the interior sequence $(h'(i))_{i \geq 0}$ and state complexity of the linear subsequence $(h(ni+c))_{i \geq 0}$. We resolve a recent question of Zantema and Bosma about linear subsequences of $k$-automatic sequences with input in most-significant-digit-first format. We also discuss the state complexity and runtime complexity of using a reasonable interpretation of Büchi arithmetic to actually construct some of the studied automata recognizing relations or carrying out operations on automatic sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complexity of Linear Subsequences of $k$-Automatic Sequences Moradi, Delaram Rampersad, Narad Shallit, Jeffrey Formal Languages and Automata Theory Discrete Mathematics Combinatorics Number Theory We construct automata with input(s) in base $k$ recognizing some basic relations and study their number of states. We also consider some basic operations on $k$-automatic sequences $(h(i))_{i \geq 0}$ and discuss their state complexity. We find a relationship between subword complexity of the interior sequence $(h'(i))_{i \geq 0}$ and state complexity of the linear subsequence $(h(ni+c))_{i \geq 0}$. We resolve a recent question of Zantema and Bosma about linear subsequences of $k$-automatic sequences with input in most-significant-digit-first format. We also discuss the state complexity and runtime complexity of using a reasonable interpretation of Büchi arithmetic to actually construct some of the studied automata recognizing relations or carrying out operations on automatic sequences. |
| title | Complexity of Linear Subsequences of $k$-Automatic Sequences |
| topic | Formal Languages and Automata Theory Discrete Mathematics Combinatorics Number Theory |
| url | https://arxiv.org/abs/2512.10017 |