Convention :  We will use small case letters towards the beginning of the English alphabet to denote symbols of an alphabet and small case letters towards the end to denote strings over an alphabet. That is,   (symbols) and    are strings.

Some String Operations :
Let and be two strings. The concatenation of x and y denoted by xy, is the string . That is, the concatenation of x and y denoted by xy is the string that has a copy of x followed by a copy of y without any intervening space between them.

Example : Concatenation of the strings 0110 and 11 is 011011 and concatenation of the strings good and boy is goodboy.

Note that for any string w, we = ew = w. It is also obvious that if | x | = n and | y | = m, then | x + y | = n + m.

u is a prefix of v if v = ux for some string x.
u is a suffix of v if v = xu for some string x.
u is a substring of v if v = xuy for some strings x and y.