Cs6503 theory of computation april may 2017
- 1. Reg. No. : B.E. / B.Tech. DEGREE EXAMINATION, APRIL / MAY 2017 Fifth Semester Computer Science and Engineering CS6503 THEORY OF COMPUTATION (Regulation 2013) Time : Three hours Maximum : 100 marks Answer ALL Questions Part A – (𝟏𝟎 × 𝟐 = 𝟐𝟎 marks) 1. Generate NFA- € to represent a*b | c. 2. Show whether a language L = { 0n 12n | n > 0} is regular or not using pumping lemma. 3. Give language of regular expression a? (a / b)*. 4. Generate CFG for a signed integer constant in C language. 5. Construct a rightmost derivation of ( a + b ) * c for using the grammar, and also state that whether a given grammar is ambiguous one or not E-> E+E /E*E/(E)/id. 6. Differentiate PDA acceptance by empty stack method with acceptance by the final sate method. 7. Write short note on Chomsky hierarchy of languages. 8. What is halting problem? 9. What is primitive recursive function? 10. Define NP completeness. Part B – (5 × 𝟏𝟔 = 𝟖𝟎 marks) 11 (a) Construct NFA with epsilon for the RE = (𝑎/𝑏 )*𝑎𝑏 and convert into DFA and further find the minimized DFA. Or (b) Prove for every 𝑛 >= 1 by mathematical induction ∑ 𝑖3 = {𝑛(𝑛 + 1)/2}2𝑛 1 . 12 (a) Given the CFG G, find CFG G’ in CNF generating the language L(G) – {^}. S → AACD A → aAb | ^ C → aC | a D → aDa | bDb | ^ Or (b) Concert the following grammar G into Greibach Normal Form (GNF). S → XA | BB B → b | SB X → b A → a QuestionPaper Code : 71684
- 2. 13 (a) (i) Construct a Deterministic Push down Automata for even length palindrome. (ii) Prove – If PDA P is constructed from CFG G by the above construction, then 𝑁(𝑃) = 𝐿(𝐺). Or (b) Convert the following CFG to PDA and verify for (a+b) and a++. I → a | b | Ia | Ib | I0 | I1 E → I | E+E | E*E| (E) 14 (a) Construct a Turing Machine to reverse the given string. Or (b) Explain Multi tape and Multi head Turing Machine with suitable example. 15 (a) Explain recursive and recursively enumerable languages with suitable example. Or (b) Explain tractable and intractable problem with suitable example. All the Best – No substitute for hard work. Mr. G. Appasami SET, NET, GATE, M.Sc., M.C.A.,M.Phil., M.Tech.,(P.hd.), MISTE, MIETE, AMIE, MCSI, MIAE, MIACSIT, MASCAP, MIARCS, MISIAM, MISCE, MIMS, MISCA, MISAET, PGDTS, PGDBA, PGDHN, PGDST, (AP / CSE / DRPEC).