Consider the following five languages. (a) L_1 = {a^i b^j | i, j elementof Z^+,

Question

Consider the following five languages. (a) L_1 = {a^i b^j | i, j elementof Z^+, j greaterthanorequalto 5i + 3} (b) L_2 = {w elementof {a, b}* | w contains the substring ab at least once, but no more than 10 times} (c) L_3 = {a^i b^j c^k | i, j, k elementof Z^nonneg, j > i, k > i} (d) L_4 = {a^i | i elementof Z^nonneg, i lessthanorequalto 100, and i is a multiple of 5} (e) L_5 = {a^i b^j | i, j elementof Z^nonneg, 3i = 2j} For each language, indicate whether it is: finite regular, but not finite context-free, but not regular not context-free You do not have to provide any proofs or construct any automata, grammars, or regular expressions, but in order to come up with your answers, you should think about which of the models we've discussed would be able to handle each language.

Explanation / Answer

The required information is given below:

i) Here L1 having the context-free but its not look like regular. Here j >= 5i + 3
ii) Here L2 language is regular but not finite.
iii) L3 language is not context-free.
iv) L4 language is a finite language. because its having i <=100 and i is multiple of 100
v) L5 is regular but not finite. Not finite because 3i = 2j

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