| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 83 === Let X be a finite alphabet and let X* be the free monoid
generated by X. Let 1 denote the empty and let X+=X*-{1}. Any
element of X* is called a word or a string and any subset of X*
is called a language. For any word w in X*, the length of w is
denoted by lg(w), that means, the number of letters occurring
in w. A nonempty word u belongs to X+ is called a primitive if
u = fn, f belongs to X+, n greater than 1, implies n = 1. A
nonempty word w is said to be overlapping if w = ux = yu for
some x, y belongs to X*, u not equal to 1,w. And u is called a
bifix of w. A nonempty word that is not overlapping is called
nonoverlapping or d-primitive. Let Q be the set of all
primitive words, and let D(1) be the set of all d-primitive
words. Two words u, v belongs to X* are conjugate if u = xy, v
= yx for some x,y belongs to X*. Let c(w) the conjugate class
of w be the set of all the words u belongs to X* such that u, w
are conjugate. A word w is called a palindrome word if its
mirror image equals to itself. A word w is called a skew-
palindrome if its mirror image is in its conjugate class c(w).
A mapping h from X* to X* is called a homomorphism if h(uv) = h(
u)h(v) for all u,v belongs to X*. If G is a family of language
over X and if h(A) belongs to G for all A belongs to G, then we
say that h preserves G or h is a G-preserving homomorphism. In
the first part of this thesis, we discuss some proporties of
palindrome words, palindrome languages and weakly palindrome
languages. In the end of section 2, we find the relation
between the length of a word w and the number of conjugate
class c(w). Secondly, we introduce a new kind of words called
skew-palindrome words. We have some proporties about skew-
palindrome words and we use them to prove results about
Fibonacci languages. Finally, we defined a new code called d-
code. We obtained the conditions on homomorphisms that preserve
palindrome words, skew-palindrome words and d-primitive words
respectively. Moreover, the conditions for D
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