A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string over the alphabet. A string that consists of a sequence a_{1}, a_{2}, . . . , a_{n} of symbols will be denoted by the juxtaposition a_{1}a_{2} a_{n}. Strings that have zero symbols, called empty strings, will be denoted by .
{0, 1} is a binary alphabet, and {1} is a unary alphabet. 11 is a binary string over the alphabet {0, 1}, and a unary string over the alphabet {1}.
11 is a string of length 2, |ε| = 0, and |01| + |1| = 3.
Example-The string consisting of a sequence αβ followed by a sequence β is denoted αβ. The string αβ is called the concatenation of α and β. The notation α^{i} is used for the string obtained by concatenating i copies of the string α.