To generate a string in the language, one begins with a string consisting of only a single
start symbol, and then successively applies the rules (any number of times, in any order) to rewrite this string. This stops when a string containing only terminals is obtained. The language consists of all the strings that can be generated in this manner. Any particular sequence of legal choices taken during this rewriting process yields one particular string in the language. If there are multiple different ways of generating this single string, then the grammar is said to be
ambiguous. For example, assume the alphabet consists of a and b, with the start symbol S, and we have the following rules: : 1. S \rightarrow aSb : 2. S \rightarrow ba then we start with S, and can choose a rule to apply to it. If we choose rule 1, we replace S with aSb and obtain the string aSb. If we choose rule 1 again, we replace S with aSb and obtain the string aaSbb. This process is repeated until we only have symbols from the alphabet (i.e., a and b). If we now choose rule 2, we replace S with ba and obtain the string aababb, and are done. We can write this series of choices more briefly, using symbols: S \Rightarrow aSb \Rightarrow aaSbb \Rightarrow aababb. The language of the grammar is the set of all the strings that can be generated using this process: \{ba, abab, aababb, aaababbb, \dotsc\}. ==See also==