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 we obtain a string containing only terminals. 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 and, with the start symbol, and we have the following rules:
then we start with, and can choose a rule to apply to it. If we choose rule 1, we replace with and obtain the string . If we choose rule 1 again, we replace with and obtain the string . This process is repeated until we only have symbols from the alphabet (i.e., and ). If we now choose rule 2, we replace with and obtain the string, and are done. We can write this series of choices more briefly, using symbols: . The language of the grammar is the set of all the strings that can be generated using this process: .
Read more about this topic: Production (computer Science)
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