Construct right- and left-linear grammars for the language L = {a^n b^m: n greaterthanorequalto 3, m greaterthanorequalto 2}. For sigma = {a, b}, find regular expressions for the complement of the following languages L = L(aa*bb*). Use the construction in Theorem 4.1 to find nfa's that accept L(b*aab*) Intersection L(baa*). a) Given a regular language L and a string w elementof L, show how one can determine if w^R elementof L. b) Show that there exists an algorithm for determining if L_1 is a proper subset of L_2, for any regular languages L_1 and L_2. Show that the language L = {a^n b^k c^n: n greaterthanorequalto 0, k greaterthanorequalto 0}is not regular. Determine whether or not the following languages are regular. a) L = {a^n b^n: n greaterthanorequalto 1} Union {a^n b^m: n greaterthanorequalto 1, m greaterthanorequalto 1} b) L = {a^n b^n: n greaterthanorequalto 1} Union {a^n b^n + 2: n greaterthanorequalto 1}