Suppose we want to tell whether a particular string s is in the language of some syntactic category .
a) Explain why, if on some round, all the new strings generated for any syntactic category are longer than s, and s has not already been generated for L(), then s cannot ever be put in L(). Hint: Use Exercise 11.3.5.
b) Explain why, after some finite number of rounds, we must fail to generate any new strings that are as short as or shorter than s.