computer theory.

Find an unrestricted grammar that generates the language L -(a" b a" b Im.n 2 0) Hint first derive a grammar that will achieve the requisite number (including zero) of a's and b's, and then add rules that can shift them into their respective places 1. 2. (a) Prove that the language Lo IR(M) w I machine M halts with input w is 'recursively enumerable 3. For the operations Union, Intersection, Concatenation, Complementation, and Kleene Star, determine 4. For the operations Union, Intersection, Concatenation, Complementation, and Kleene Star. determine (b) Prove that Ls is not "recursive and justify the closure (or non-closure) properties for Recursively Enumerable Languages. and justify the closure (or non-closure) properties for Recursive Languages