On Concatenations of Regular Circular Word Languages

Bilal Abdallah () and Benedek Nagy ()
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Bilal Abdallah: Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, 99450 Famagusta, North Cyprus, Mersin-10, Turkey
Benedek Nagy: Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, 99450 Famagusta, North Cyprus, Mersin-10, Turkey

Mathematics, 2025, vol. 13, issue 5, 1-14

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.

Keywords: circular words; conjugate class; cyclic words; regular expressions; finite automata; weak and strong acceptance; formal languages (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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