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 .