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Abstract
A word u is said to be an n-power prefix of another word w if w∈u
n
X*. Let P
i
denote the family of words which have i-power prefixes but no (i+1)-power prefix. Words in P
1 are called p-primitive words. In this paper, some basic properties of words in sets and P
i
are studied. It is shown that the sets P
i
, P
i
\ Q, P
i
∩Q, Q\ P
i
,
and P
i
∪Q for i≥1 are disjunctive. That is, they are dense non-regular languages. A characterization of words in
for i≥2 is derived. Several properties of words in
are considered too.
AMS Subject Classification::
Acknowledgements
This work was supported by the National Science Council R.O.C. under Grant NSC 93-2115-M-005-006.