On Concatenations of Regular Circular Word Languages
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| Publicado en: | Mathematics vol. 13, no. 5 (2025), p. 763 |
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| Autor principal: | |
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| Publicado: |
MDPI AG
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| Resumen: | In this paper, one-wheel and two-wheel concatenations of circular words and their languages are investigated. One-wheel concatenation is an operation that is commutative but not associative, while two-wheel concatenation is associative but not commutative. Moreover, two-wheel concatenation may produce languages that are not languages of circular words. We define two classes of regular languages of circular words based on finite automata: in a weakly accepted circular word language, at least one conjugate of each word is accepted by the automaton; in contrast, a strongly accepted language consists of words for which all conjugates are accepted. Weakly accepted circular word languages <inline-formula>REGw</inline-formula>, in fact, are regular languages that are the same as their cyclic permutations. Strongly accepted circular word languages, <inline-formula>REGs</inline-formula>, having words with the property that all their conjugates are also in the language, are also regular. We prove that <inline-formula>REGw</inline-formula> and <inline-formula>REGs</inline-formula> coincide. We also provide regular-like expressions for these languages. Closure properties of this class are also investigated. |
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| ISSN: | 2227-7390 |
| DOI: | 10.3390/math13050763 |
| Fuente: | Engineering Database |