For a regular language L, the power of L is the least (nonnegative) integer p for which U = U+1, if such p exists, and oo otherwise 4 (a) Consider an arbitrary regular language L over the alphabet 10,1 Prove that the power of L is finite if and only if there is a nonnegative integer k such thst L, and that in this case, the power of L is the least k such that Lk-L' (b) what is the power of the regular language 00)(000).? Justify your answer. (c) What is the power of the regular language a U o0) 000? Justify your answer. (d) What is the power of the language denoted /represented by the regular expression (E 10)(1 +01*01 0)*? Justify your answer. For a regular language L, the power of L is the least (nonnegative) integer p for which U = U+1, if such p exists, and oo otherwise 4 (a) Consider an arbitrary regular language L over the alphabet 10,1 Prove that the power of L is finite if and only if there is a nonnegative integer k such thst L, and that in this case, the power of L is the least k such that Lk-L' (b) what is the power of the regular language 00)(000).? Justify your answer. (c) What is the power of the regular language a U o0) 000? Justify your answer. (d) What is the power of the language denoted /represented by the regular expression (E 10)(1 +01*01 0)*? Justify your