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Báo cáo toán học: " Some Periodicity of Words and Marcus Contextual Grammars"

Sau khi chúng tôi xác định một số Marcus ngữ pháp theo ngữ cảnh, chúng tôi cho thấy rằng các thiết lập của tất cả các từ nguyên thủy (mạnh nguyên thủy, siêu nguyên thủy) có thể được tạo ra bởi một số ngữ pháp theo ngữ cảnh của Marcus. | Vietnam Journal of Mathematics 34 4 2006 381-387 Viet n a m J o u r n a I of MATHEMATICS VAST 2006 Some Periodicity of Words and Marcus Contextual Grammars Pal Domosi1 Geza Horvath1 Masami Ito2 and Kayoko Shikishima-Tsuji3 1. . 2. 3. Dedicated to Professor Do Long Van on the occasion of his 65th birthday Received June 23 2006 Revised July 23 2006 Abstract. In this paper first we define a periodic semi-periodic quasi-periodic word and then we define a primitive strongly primitive hyper primitive word. After we define several Marcus contextual grammars we show that the set of all primitive strongly primitive hyper primitive words can be generated by some Marcus contextual grammar. 2000 Mathematics Subject Classification 68Q45. Periodicity of words primitive words strongly primitive words hyper primitive words Marcus contextual grammars. 1. Introduction Let denote the free monoid generated by a nonempty finite alphabet and let where denotes the empty word of . For the sake of This work was supported by the grant of the Japan-Hungary Joint Research Project organized by the Japan Society for the Promotion of Science and the Hungarian Academy of Science the Hungarian National Foundation for Scientific Research OTKA T049409 and the Grant-in-Aid for Scientific Research No. 16-04028 Japan Society for the Promotion of Science. 382 Pá Domosi Géza Horvath Masami Ito and Kayoko Shikishima-Tsuji simplicity if then we write and instead of. and respectively. Let then is called a over . Let then is called a.over . By we denote the cardinality of . If then denotes the set of all concatenations of words in and . In particular if then we write and instead of. and respectively. Definition 1.1. . . v . . . 2. Fig. 1.1 indicates that is a periodic word. Definition 1.2 . . . . Fig. 1.2 indicates that is a semi-periodic word. 2 Definition 1.3. . . . . . . . Fig. 1.3 indicates that is a quasi-periodic word. V V V V V Some Periodicity of Words and Marcus Contextual Grammars 383 Then we have