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On Concatenations of Regular Circular Word Languages

Author

Listed:
  • Bilal Abdallah

    (Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, 99450 Famagusta, North Cyprus, Mersin-10, Turkey
    Department of Mathematics and Statistics, American University of the Middle East, Egaila 54200, Kuwait)

  • Benedek Nagy

    (Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, 99450 Famagusta, North Cyprus, Mersin-10, Turkey
    Department of Computer Science, Institute of Mathematics and Informatics, Eszterházy Károly Catholic University, 3300 Eger, Hungary)

Abstract

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 R E G w , in fact, are regular languages that are the same as their cyclic permutations. Strongly accepted circular word languages, R E G s , having words with the property that all their conjugates are also in the language, are also regular. We prove that R E G w and R E G s coincide. We also provide regular-like expressions for these languages. Closure properties of this class are also investigated.

Suggested Citation

  • Bilal Abdallah & Benedek Nagy, 2025. "On Concatenations of Regular Circular Word Languages," Mathematics, MDPI, vol. 13(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:763-:d:1600232
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