Circularity and repetitiveness in non-injective DF0L systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911095616176128 |
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| author | Goulet-Ouellet, Herman Klouda, Karel Starosta, Štěpán |
| author_facet | Goulet-Ouellet, Herman Klouda, Karel Starosta, Štěpán |
| contents | We study circularity in DF0L systems, a generalization of D0L systems. We focus on two different types of circularity, called weak and strong circularity. When the morphism is injective on the language of the system, the two notions are equivalent, but they may differ otherwise. Our main result shows that failure of weak circularity implies unbounded repetitiveness, and that unbounded repetitiveness implies failure of strong circularity. This extends previous work by the second and third authors for injective systems. To help motivate this work, we also give examples of non-injective but strongly circular systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Circularity and repetitiveness in non-injective DF0L systems Goulet-Ouellet, Herman Klouda, Karel Starosta, Štěpán Discrete Mathematics 68R15, 68Q42 We study circularity in DF0L systems, a generalization of D0L systems. We focus on two different types of circularity, called weak and strong circularity. When the morphism is injective on the language of the system, the two notions are equivalent, but they may differ otherwise. Our main result shows that failure of weak circularity implies unbounded repetitiveness, and that unbounded repetitiveness implies failure of strong circularity. This extends previous work by the second and third authors for injective systems. To help motivate this work, we also give examples of non-injective but strongly circular systems. |
| title | Circularity and repetitiveness in non-injective DF0L systems |
| topic | Discrete Mathematics 68R15, 68Q42 |
| url | https://arxiv.org/abs/2504.15828 |