copy of w on the tape immediately after w,leaving the string w#w on the tape.Assume that the input string initially appears at the left most end of the tape and that the input alphabet does not contain the blank character’ : The end of the input string is therefore determined by the location of the first blank cell on the input tape. The symbol # is assumed to be in the tape alphabet,and the input alphabet is {a,b}. (12) b)Demonstrate the working of your TM with an example. (4) 20.a)Show that the language{0n 1n 2n/n>=1}is not context free. (8) b)Show that the context free languages are closed under union operation but not under intersection. (8) UNIT-V UNDECIDABILITY PART-A 1When a recursively enumerable language is said to be recursive. 2Is it true that the language accepted by a non deterministic Turing Machine is different from recursively enumerable language? 3When we say a problem is decidable? Give an example of undecidable problem? 4Give two properties of recursively enumerable sets which are undecidable.

5Is it true that complement of a recursive language is recursive? Justify your answer. 6When a language is said to be recursive or recursively enumerable? 7When a language is said to be recursive? Is it true that every regular set is not recursive? 8When a problem is said to be decidable or undecidable? Give an example of an undecidable. 9What do you mean by universal Turing Machine? 10.When a problem is said to be undecidable? Give an example of an decidable problem. 11.Show that the union of recursive language is recursive. 12.Show that the union of two recursively enumerable languages is recursively enumerable. 13.What is undecidability problem? 14.Show that the following problem is undecidable.“Given two CFG’s G1 and G2, is L(G1)∩L(G2)=Φ?”. 15.Define Ld. 16.Define recursively enumerable language. 17.Give an example for a non recursively enumerable language. 1Differentiate between recursive and recursively enumerable languages. 2Mention any two undecidability properties for recursively enumerable language. 21.Define Diagonal languages. 22.Give an example for an undecidable problem. PART-B 1.a)Show that union of recursive languages is recursive. (4) b)Define the language Ld and show that Ld is not recursively enumerable language. (8) c)Explain the Halting problem. Is it decidable or undecidable problem (4) 2.Define Universal language Lu.Show that Lu is recursively enumerable but not recursive.