Is it possible to prove that L is a regular language?
Let L = {a^f(m) | m >= 1 }
where f: Z^+ -> Z^+
is monotone increasing and complies that for all element n
in Z^+
there is an m开发者_运维知识库
belonging to Z^+
such that f(m+1) - f(m) >= n
.
Is it possible to prove that L is a regular language?
Let f(x) = 2^x. For any positive n, f(n+1) - f(n) >= n.
L = {a^f(m)} is not regular. Consider the strings a^(2^x + 1). After an FA processes such a string, the smallest string which leads to an accepting state is a^(2^x - 1), having length 2^x - 1. Therefore, a separate state will be needed for every value of x. Since there are infinitely many values of x (positive integers), no FA exists to recognize L; ergo, L is not a regular language.
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