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Powers of Strings : For any string x and integer , we use to denote the string formed by sequentially concatenating n copies of x. We can also give an inductive definition of as follows:
= e, if n = 0 ; otherwise ![](eqns/eq-65.gif)
Example : If x = 011, then = 011011011, = 011 and ![](eqns/e-16.gif) Powers of Alphabets :
We write (for some integer k) to denote the set of strings of length k with symbols from . In other words,
= { w | w is a string over and | w | = k}.
Hence, for any alphabet, denotes the set of all strings of length zero. That is, = { e }. For the binary alphabet { 0, 1 } we have the following.
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