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- Automata Theory And Computability - ATC
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Printed Pages: 4 NCS-4A2N,CS-403 (Following Paper ID and RoIl No. to be filted in your Answer Books) RoII No B.TECH. Theory Examination (Semester-fn 2015-1 6 THE ORY OF AUTOU,AIA AI\D FORIVIATLAUNGUAGE Time.' 3 Hours Max. Marks: 100 Section-A QJ Attempt aII parts. AII parts carry equal marks. Write answer of each part in short Qxl0:20) (a) Design a EA to accept the string that always ends with 00. (b) Differentiate between the L* and Li. (c) Write regular expression for set of all strings such that number of 0's is odd. (d) What is a Moore and Mealy'machine? ls38l13450

(e) Constnict the CFG for the regular expression (0+l)*. (0 What are the features of universat Turing machine? G) Define the languages generated by Turing machine. (h) Describe the instantaneous description of a PDA. (i) Design a DFA to accept the binary number divisible by fi) 3. What do you understand by Epsilon-closure of sate in finite automata? Seetion-B 2. Attempt any five parts. AtI parh carry equal marlcs: (5*10=50) Construct a IrtFA for the language L which accept all the strings in which the third synrbol from right end is always an over E {a. : b. b}. , State ard Prove Fumpirâ‚¬,Lemrna of RE. Show that f- {ap : p is prime) is not regular? c. Explain the parse tree with an exarnple. Reduce the context free grammar into GNF whose productions are S-+aSb. S-+ab. 1538/13450

d. Define Pushdown automata. Differentiate PDA by empty stack and final state by giving their definitions. g. Obtain PDA to accept all strings generated by the lang,rage {a"b*an, f. mrn}-l }. Construct DHA eauivalent to NFA. where E is defined in the following table: I a 6(q,a) 6(q,b) A A,B C B A B C*(final stale) A,B Table: I consider the cFG ({s, A, productions Pare as follows: B} {a,b}, p,s) where I S->aABB/ aAIA, A+aBBla,B-+bBB / A.Convert the given graulmar to PDA that accqpt the $ame language by empty stack. Design CFG for the langrrage consisting of all strings of even length over {a, b}. I '1, ,. s3gl1 34s0

Section-C Note:Attempt any two questions from this section. (2x15:30) \ 3. 4. Write short notes on the following: (a) Halting Problem (b) Chtlrch's (c) Recrusively enumerable lansmge thesis 'i What is Chomsky hierarchy? Explain post correspondence problem. 5, Consfiuct a Turing machine which accepts the regutar expression, L {01' ln>: 1}. - ,l 1 i I i I 'l I t I I I I :{:i 1 '| I i ..* 1' i I l 'l ,i :i ,! I 1538113450 '\r

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