Alphabets, Strings and Languages
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Example : 0110, 11, 001 are three strings over the binary alphabet { 0, 1 } .

aab, abcb, b, cc are  four strings over the alphabet { a, b, c }.

It is not the case that a string over some alphabet should contain all the symbols from the alphabet. For example, the string cc over the alphabet { a, b, c } does not contain the symbols a and b. Hence, it is true that a string over an alphabet is also a string over any superset of that alphabet.

 

Length of a string :
The number of symbols in a string w is called its length, denoted by |w|.

Example : | 011 | = 4,  |11| = 2,  | b | = 1

It is convenient to introduce a notation e for the empty string, which contains no symbols at all. The length of the empty string e is zero, i.e., | e | = 0.

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