Properties Of Some Words

The purpose of this thesis is to construct some kinds of prefix primitive words and establish disjunctive language associated with prefix primitive words. In2004, the scholars C. C. Huang and S. S. Yu from Taiwan got the conclusion:if the length of word v is longer than that of word u and uv3is a prefix primitive word, then every word in the language uv+is a prefix primitive word. We show that if the length of the word u is between the length of word v and3v, and v, uv3are p-primitive words, then every word in uv+is a prefix primitive word. Their another result:Let p be a primitive word and integer k≥3. If the length of the word pk is longer than that the length of the word u, and upk is a prefix primitive word, then every word in up+is a prefix primitive word. We obtain the same conclusion when I change the condition that the length of the word pk is longer than that of the word u as that word pk is not the infix of word u. In2011, scholar Z. Z. Li and scholar Y. S. Tsai proved that the set of all primitive words which lengths are divided by n and the reminders are r is a disjunctive language. In this thesis, we prove that the set of all prefix primitive words which lengths are divided by n and the reminders are r is also a disjunctive language.