The input string is denoted by x.
|x| is the length of x.
Individual input symbols are identified
by indices starting at 0: 
.
The input alphabet is denoted by 
.
Substrings are identified by beginning and end positions 
.
The variables i, j, k are reserved for integers referring to positions in
input strings.
Latin capital letters X, Y, Z denote nonterminal symbols.
Latin lowercase letters 
are used for terminal symbols.
Strings of mixed nonterminal and terminal symbols are written using
lowercase Greek letters 
.
The empty string is denoted by 
.