Theory of Computation

Year : 2015-16

UNIT-I Finite Automata

Sem. : ODD

Subject Code

: CS6503

Branch

: CSE

Subject Name

: Theory of Computation

Year/Sem.

: III/V

PART-A 1. Any set A, B and C if AnB=Ø and C B then AnC=Ø. Prove by contra positive. (Apr/May 2015) 2. Prove for every n>=1 by mathematical induction. (Apr/May 2015)

3. Give English description of the following language (0+1))*1*. (Apr/May 2015) 4. Construct NFA -^ for 1*(01)* (Apr/May 2015) 5. Design DFA to accept strings over Σ= (0,1) with two consecutive 0‟s. (Nov/Dec 2014) 6. Prove or disprove that (r+s)*=r*+s* (Nov/De 2014) 7. State the pumping lemma for regular languages. (Nov/Dec 2014) 8. What is finite automaton? (May/June 2014) 9. Enumerate the difference between DFA and NFA (May/June 2014) 10. Draw the transition diagram (automata) for an identifier. (Nov/Dec 2013) 11. What is a non deterministic finite automaton? (Nov/Dec 2013) 12. What is meant by DFA? (Apr/May 2013) 13. Define the term Epsilon transition. (Apr/May 2013) 14. State the principle of induction. (Nov/Dec 2012) 15. Define: (a) Finite Automaton (FA) (b) Transition diagram (Nov/Dec 2012) 16. What is a regular expression? (May/June 2013) 17. State the difference between NFA and DFA. (Nov/Dec 2011) 18. Define ε-closure (q) with an example. (May/June 2012) 19. Name any for closure properties of Regular languages. (May/June 2013) 20. Construct NFA for the regular expression a*b*. (May/June 2012) 21. Is regular set is closed under complementation? Justify. (May/June 2012) 22. Give regular expression for the following  L1=set of all strings of 1 and 0 ending in 00  L2=set of all stings of 0 and 1 beginning with 0 and ending with 1. (Nov/Dec 2012) 23. Differentiate regular expression and regular language. (Nov/Dec 2012) 24. Construct a DFA for the following:  All strings that contain exactly 4 zeros  All strings that don‟t contain the substring 110. (Nov/Dec 2011 25. Is the set of strings over the alphabet {0} of the form 0n where n is not a prime is regular? Prove or disprove. (Nov/Dec 2011) 26. State pumping lemma for regular languages. (Nov/Dec 2013) 27. Construct NFA equivalent to regular expression (0+1)01. (Nov/Dec 2013) 28. Give the regular expression for set of all strings ending in 00. (Nov/Dec 2010) 29. State pumping lemma for regular set. (Nov/Dec 2010)

30. Construct a finite automaton for the regular expression 0*1* (May/June 2014) 31. Mention the closure properties of regular languages. (May/June 2014)

PART-B

1. Prove that for every integer n≥0 the number 42n+1 and 3n+2 is a multiple of 13. (Nov/Dec 2014) 2. Let L be a set accepted by a NFA and then prove that there exists a DFA that accepts L. (Nov/Dec 2014) 3. Construct a DFA equivalent to the NFA M=({a, b, c, d} ,{0,1}, δ, a,{b. d} ) where δ is defined as(Nov/Dec2014) δ 0 1 a {b, d} {b} b C {b, c} c d a d a 4. 5. 6. 7.

Construct a minimized DFA for the RE 10+ (0+11)0*1. (Nov/Dec 2014) Show that L= {0n2 /is an integer, n≥1} is not regular. (Nov/Dec 2014) Explain the DFA minimization algorithm with an example. (Nov/Dec 2014) Design a DFA accepts the following strings over the alphabets {0, 1} The Set of all strings that contains a pattern 11. Prove this using mathematical induction. (May/June 2015) 8. Design a NFA accepts the following strings over the alphabets {0, 1}. The set of all string that begins with 01 and end with 11. Check for the validity of 01111 and 0110 strings. (May/June 2015) 9. Find the min-state DFA for (0+1)*10. (May/June 2015) 10. Find the regular expression of a language that consist of set of string starts with 11 as well as ends with 00 using Rij formula.(May/June 2015) 11. Construct a DFA accepting all strings w over {0,1} such that the number of 1‟s in w is 3 mod 4 (Nov/Dec 2011) 12. Construct a minimized DFA from the regular expression (x+y) x (x+y)*. Trace for a string w=xxyx.(Nov/Dec 2011) 13. State and explain the conversion of DFA into regular expression using Arden‟s theorem. Illustrate with an example.(Nov/Dec 2011) 14. Prove by induction on n that (Apr/May 2012) 15. Construct a DFA accepting binary strings such that the third symbol form the right end is . (Apr/May 2012) 16. Construct a NFA without ε-transitions for the NFA given below. (Apr/May 2012)

17. Prove the following by the principle of induction (Apr/May 2015)

18. Discuss on regular expressions.(8)(May/June 2013) 19. Construct an NFA accepting binary strings with two consecutive 0‟s. (Apr/ May 2012)

20. Construct a DFA that accepts all strings on {0,1} except those containing the substring 101.(April/May 2014) 21. Prove that if L is accepted by an NFA with ε- transitions then L is accepted by an NFA without ε transitions.(Nov/Dec 2012) 22. Prove that if n is positive integer such that n mod 4 is 2 or 3 then n is not a perfect square.(Nov/Dec 2012) 23. Discuss on the relation between DFA and minimal DFA. (Apr/May 2013) 24. Write a note on NFA and compare with DFA.(Apr/May 2013) 25. Convert the following NFA to DFA(Apr/May 2013)

26. Construct DFA to accept the language L={w| w is of even length and begins with 11} ( Apr/May 2013) 27. Construct a DFA that accept the following language. {x € {a,b}|x|a = odd and |x|b =even. (Nov/Dec 2012) 28. Construct a non deterministic finite automaton for accepting the set of strings over {a,b} ending in aba. Use it to construct a DFA accepting the same set of strings. (Apr/May 2014) 29. Construct a NFA with ε moves which accepts a language consisting the strings of any number of a‟s, followed by any number of b‟s, followed by any number of c‟s. (Apr/May 2014) 30. Explain the steps in conversion of NFA to DFA. Convert the following NFA to DFA. (Nov/Dec 2013)

31. Prove that the following languages are not regular.  {02n|n≥1}  {ambna m+n|m≥1 and n≥ 1} (May/June 2013) 32. Discuss on equivalence and minimization of automata. (Nov/Dec 2013) 33. Prove that if L is accepted by an NFA with ε transitions, then L is accepted by NFA without ε transitions. (Nov/Dec 2013) 34. Prove the equivalence of NFA and DFA using subset construction .(Nov/Dec 2013)

35. Give Deterministic finite automata accepting the following language over the alphabet. (Nov/Dec 2013) (1) Number of 1‟s is a multiples of 3 (2) Number of 1‟s is not a multiples of 3 36. Obtain minimized finite automaton for the regular expression (b/a)*baa. (May/June 2012) 37. Prove that there exists an NFA with є-transitions that accepts the regular expression r. (May/June 2012) 38. Which of the following languages is regular? Justify.(May/June 2012)  L={anbm/n,m≥ 1}  L={anbn/n≥1} 39. Obtain the regular expression for the finite automata.(May/June 2012)

40. Using pumping lemma for the regular sets, prove that the language L={ambn|m>n} (Nov/Dec 2012) 41. Prove any two closure properties of regular languages. (Nov/Dec 2012) 42. Construct a minimized DFA that can be derived from the following

regular expression 0*(01)(0/111)*. (Nov/Dec 2012) 43. Design a finite automaton for the regular expression (0+1)*(00+11)(0+1*). (May/June 2014) 44. Prove that L={0 i2/i is an integer; i≥ 1} is not regular. (May/June 2014) 45. Prove that the class of regular sets is closed under complementation. (May/June 2014) 46. Let r be a regular expression. Prove that there exists an NFA with єtransitions that accepts L(r). (Nov/Dec 2010) 47. Is the language L= {anbn|n≥1} is regular? Justify. (Nov/Dec 2010) 48. Construct the minimal DFA for the regular expression (b|a)*baa. (Nov/Dec 2010) 49. Prove that regular sets are closed under substitution. (Nov/Dec 2010) 50. State and explain the conversion of DFA to regular expression using Arden‟s theorem. Illustrate with an example. (Nov/Dec 2013) 51. Convert the following NFA into a regular expression.(Nov/Dec 2013)

52. Discuss the closure properties of regular languages(8)(Nov/Dec 2013) 53. Using pumping lemma for regular sets prove that the language

L={0m1n0m+n|m≥1 and n≥1} is not regular.(Nov/Dec 2013)

Year : 2014-15

UNIT-II Grammars

Sem. : ODD

Subject Code

: CS6503

Branch

: CSE

Subject Name

: Theory of Computation

Year/Sem.

: III/V

PART-A 1. Give the general forms of CNF.(Nov/Dec 2014) 2. Show that CFLs are closed under substitutions. (Nov/Dec 2014) 3. Let G be the grammar S->aB/bA A->a/aS/bAA B->b/bS/aBB. For the string aaabbabbba, find (a) LMD and (b) RMD (Nov/Dec 2014) 4. Generate CFG for (011+1)* (May/June 2015) 5. Construct a parse tree of (a+b)*c for the grammar E->E+E/E*E/(E)/id (May/June 2015)

6. Define pumping lemma for CFL.(May/June 2015) 7. Construct a CFG for the language of palindrome strings over {a,b} May/June 2014 8. When do you say a grammar is ambiguous? (May/June 2014 9. Write the CFG for the language L= {anbn/n≥1}. (Nov/Dec 2013 10. What is a CFG? (May/June 2013) 11. Define the term Ambiguity in grammars. (May/June 2013) 12. What is an ambiguous grammar? Give example. (Nov/Dec 2012) 13. Specify the use of context free grammar. (May/June 2012) 14. Define parse tree with an example. (May/June 2012) 15. Is the grammar below ambiguous S->SS/(S)/S(S)S/E? (Nov/Dec 2011) 16. Convert the following grammar into an equivalent one with no unit productions and no useless symbols S->ABA, A->aAA/aBC/bB, B->A/bB/Cb, C->CC/cC. (Nov/Dec 2011) 17. Write down the context free grammar for the language L={anbn/n≥1}. (Nov/Dec 2010) 18. Is the grammar E->E+E/id is ambiguous? Justify. (Nov/Dec 2010) 19. Consider the following grammar G with productions S->ABC/BaB, A->aA/BaC/aaa, B->bBb/a, C->CA/AC. Give a CFG with no useless variables that generates the same language. (Apr/May 2010) 20. Find out the context free language S->aSb/aAb A->bAa A->ba (May/June 2009) 21. Show that the grammar S->a/Sa/bSS/SSb/SbS is ambiguous.Nov/Dec 2008 22. Find whether the language {ambmcm, m≥0} is context free or not. (Nov/Dec 2008) (Nov/Dec2007) 23. Let S->aB/bA, A->aS/bAA/a, B->bS/aBB/b Derive the string “aaabbabba” as left most derivation. (Apr/May 2008) 24. Let the productions of a grammar be S->0B/1A, A->0/0S/1AA, B->1/1S/0BB. For the string 0110 find a rightmost derivation .May/June 2007 25. Write a CFG to generate the set {ambncp/m+n=p and p≥ 1}.Nov/Dec 2006 26. Consider the alphabet ∑={a,b,(,),+,*,.,-}.Construct the context free grammar that generates all strings in ∑ * that are regular expression over the alphabet {a,b}.

27. What are the closure properties of CFL? (NOV/DEC-2013, MAY/JUNE-2013) 28. What is meant by Greibach Normal Form? (MAY/JUNE-2013, NOV/DEC-2009, MAY/JUNE2009) 29. What is Chomsky normal form? (MAY/JUNE-2012) 30. State the two normal forms and give an example. (NOV/DEC-2011) 31. Is the language L={anbncn|n>=1} context free? Justify. (NOV/DEC-2010) 32. Convert the following grammar G in Greibach normal form: S->ABb|a; A->aaA|B; B->bAb. (MAY-2010) 33. Find whether the language {ambmcm,m>=0} is context free or not. (NOV/DEC-2007) 34. What is the class of language for which the TM has both accepting and rejecting configuration? Can this be called a context free language? (NOV/DEC-2006)

PART-B 1. Given the CFG G, find CGF G in CNF generating the language.L(G)-{^) s-> AACD, A-> aAb|^, C->aC|a, D-> aDa|bDb|^. (May/June 2015) 2. If G is the grammar S->SbS/a show that G is ambiguous. (May/June 2014) 3. Write a grammar G to recognize all prefix expressions involving all binary arithmetic operators. Construct a parse tree for the sentence “-*+abc/de” using G? (Nov/Dec2014) 4. Show that the following grammar G is ambiguous S->SbS/a. (Nov/Dec 2014) 5. Construct a context free grammar for {0m1n/1≤m≤n} (Nov/Dec 2014) 6. Find a grammar G in CNF form equivalent to G S->aAD, A->aB/bAB, B->b, D->d. (Nov/Dec 2014) 7. Convert the grammar S->0S1/A;A->1A0/S/ϵ into PDA that accepts the same language by empty stack .Check whether 0101 belongs to N(M). (May/June 2014) 8. Convert to GNF the grammar G, G=({A1,A2,A3},{ab},P,A1} where P consists of the following A1->A2A3 , A2->A3A1/b, A3->A1A2/a. (Nov/Dec 2014) 9. Explain about Parse trees. For the following grammar (May/June 2013) S->aB/bA A->a/aS/bAA B->b/bS/aBB For the String “aaabbabbba” ,Find (1)Leftmost derivation (2)Rightmost derivation (3)Parse tree 10. Convert the following grammar into GNF S->XY1/0 X->00X/Y Y->1X1 (Nov/Dec 2013) 11. Show that the following grammars are ambiguous. {S->aSbS/bSaS/λ} and {S->AB/aaB,A->a/Aa,B->b} (Nov/Dec 2013) 12. Consider the following grammar for list structures. S->a/˄/ (T) T->T, S/S. Find left most derivation, rightmost derivation and parse tree for (((a,a),˄(a)),a) (Nov/Dec 2012) 13. Is the grammar E->E+E/E*E/id is ambiguous? Justify your answer. (May/June 2012) 14. Find the context free languages for the following grammars. (1)S->aSbS/bSaS/ϵ (2) S->aSb/ab (May/June 2012)

15. Convert the grammar S->aSb/A,A->bSa/S/ϵ to a PDA that accepts the same language by empty stack.(10)Nov/Dec 2011 16. If S->aSb/aAb, A->bAa, A->ba is the context free grammar. Determine the context free language.(6)Nov/Dec 2011 17. Let G be the grammar S->aB/bA, A->a/aS/bAA, B->b/bS/aBB. For the string “baaabbabba” Find leftmost derivation, rightmost derivation and parse tree. (Nov/Dec 2010) 18. Consider the grammar S->iCtS, S->iCtSeS, S->a, C-> b Where i, t and e stand for if, then, and else, and C and S for “conditional” and “statement” respectively  Construct a leftmost derivation for the sentence w=ibtibtaea  Show the corresponding parse tree for the above sentence  Is the above grammar ambiguous? If so prove it.  Remove ambiguity if any and prove that both the grammar produces the same language. (Apr/May 2010) 19. Construct the CFG for the following languages: (1)L(G)={ambn/m≠n,n>0} and (2)L(G)={anban/n≥1} (3)Define Ambiguity, Leftmost derivation and with Rightmost derivation an example. (May/June 2009) 20. Simplify the following grammar and find its equivalent in CNF. (Nov/Dec 2008) S->AB/CA B->BC/AB A->a C->aB/b (Nov/Dec 2008) 21. Find the GNF equivalent of the grammar S->AA/0,A->SS/1. (Nov/Dec 2008) 22. Construct a CFG accepting L={ambn/nbAB/λ, B->Baa/λ. (Apr/May 2008) 24. Define Chomsky normal form. Find an equivalent grammar in CNF for the grammar G

= ({S, A, B}, {a, b}, P, S) with productions S->bA|aB; A->bAA|aS|a; B->aBB|bS|b. (MAY2014, NOV/DEC-2006) 25. Show that the language L= {aibici|i>=1} is not context free. (MAY-2014, MAY -2007) 26. Construct the following grammar in CNF: A->BCD|b; B->Yc|d; C->gA|c; D->dB|a; Y>f. (MAY -2013) 27. Explain about the closure properties of CFL. (MAY-2013, MAY-2012, DEC-2011, NOV2010) 28. Explain in detail about Pumping Lemma for CFL. (MAY/JUNE-2013, NOV/DEC-2012) 29. Convert the following grammar into CNF: S->cBA; S->A; A->cB; A->AbbS; B->aaa. (NOV/DEC-2012) 30. Find Greibach normal form for the grammar: S->AA|  ; A->SS| . (MAY/JUNE-2012) 31. State the pumping lemma for CFLs. What is its main application? Give two examples. (NOV-2011) 32. Prove that every grammar with productions can be converted to an equivalent grammar without productions. (MAY/JUNE-2011) 33. Reduce the following grammar to CNF: S->a|AAB; A->ab|aB| ; B->aba| . (MAY/JUNE-

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2011)

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34. Convert the following to Greibach normal form: S->a|AB; A->ab|BC; B->b; C->b. (MAY/JUNE-2011) 35. Obtain a GNF grammar equivalent to the context free grammar: S->AA|0; A->SS|1. (NOV/DEC-2010) 36. Define Pumping Lemma for CFL. Show that L = {aibjck; iC|D; B->1B|1; C>0C|0; D->2D|2. (MAY-2010) 38. Convert the grammar S->AB|aB; A->aab| ; B->bbA into CNF. (MAY/JUNE-2009) 39. Prove that the set of CFL is closed under union and kleen closure. (MAY/JUNE-2009) 40. Simplify the following grammar and find its equivalent in CNF: S->AB|CA; B->BC|AB; A->a; C->aB|b. (NOV/DEC-2008, NOV/DEC-2007) 41. Find the GNF equivalent for the grammar: S->AA|0; A->SS|1. (NOV-2008, NOV-2007 NOV-2006) 42. Show that the context free languages are closed under union operation but not under intersection. (NOV-2007) 43. Find a grammar in Chomsky normal form equivalent to S->aAbB; A->aA|a; B->bB|b. (MAY-2007) 44. Convert the grammar S->AB; A->BS|b; B->SA|a into Greibach normal form. (MAY/JUNE-2007)

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UNIT-III Push Down Automata

Year : 2014-15 Sem. : ODD

Subject Code

: CS6503

Branch

: CSE

Subject Name

: Theory of Computation

Year/Sem.

: III/V

PART-A 1. Define push down automata. 2. Differentiate PDA acceptance by empty stack method with acceptance by final state method. (May/June 2015) 3. Compare NFA and PDA. (Nov/Dec 2013) 4. What are the different types of language accepted by a PDA and define them?Nov/Dec 2012 5. State the definition for pushdown automata. (Apr/May 2010) 6. Construct a PDA to accept the language {(ab) n] n≥1} by empty stack.(Nov/Dec2009) 7. For a PDA M= , define the language accepted by final state. (Nov/Dec 2009) 8. Define instantaneous description of push down automata. (May/June 2009) 9. What is meant by empty production removal in PDA? (Apr/May 2008) 10. Define the language recognized by the push down automata using empty stack. (Nov/Dec 2007) 11. Define the languages generated by a PDA using the two methods of accepting a language. (May/June 2007) 12. Define the languages generated by a PDA using final state of the PDA and empty stack of that PDA. (Nov/Dec 2006) 13. State the definition of Push down Automata. 14. What are the different types of languages accepted by a pushdown automaton and define them? 15. Give an example of PDA. 16. Define acceptance of a PDA by empty stack. Is it true that the language accepted by a PDA empty stack or by that of final states is different languages? 17. What is the additional feature PDA has when compared with NFA? Is PDA superior over NFA in the sense of language acceptance? Justify your answer. 18. Is it true that non-deterministic PDA is more powerful than that of deterministic PDA? Justify your answer. 19. Is the language of DPDA and NPDA same? 20. Give the formal definition of a PDA. PART-B 1. Construct a PDA for the given grammar S->aSa/bSb/c. (May/June 2015) 2. Construct a PDA for the language L={x€ {a,b}* |na (x)>nb(x)} (May/June 2015) 3. If L is context free language prove that there exists a PDA M, such that L=N(M) (Nov/Dec 2014) 4. Prove that if L is N(M1)( the language accepted by empty stack) for some PDA M1, then L is N(M2) (the language accepted by final state) for some PDA M2. (Nov/Dec 2014) 5. Construct pushdown automata to accept the language L= {anbn/n≥1} by stack and by final state. (May/June 2014) 6. Construct a CFG for the PDA M. (May/June 2014) 7. Convert the grammar S->0S1/A; A->1A0/S/ϵ into PDA that accepts the same language by empty stack. Check whether 0101 belongs to N(M).(May/June 2014)

8. Construct PDA for the language L= (wwR /W in (a+b)*). (8) May/June 2013 9. Explain in detail about equivalence of pushdown automata and CFG. (May/June 2013) 10. Give formal pushdown automata that accepts {wcw R /w in (0+1)*} by empty stack. (Nov/Dec 2013) 11. Prove the equivalence of PDA and CFL. (Nov/Dec 2013) 12. Construct a transition table for PDA which accepts the language L= {a2nbn/n≥ 1}.Trace your PDA for the input with n=3. (Nov/Dec 2012) 13. Find the PDA equivalent to the given CFG with the following productions. 14. S->A, A->BC, B->ba,C->ac. (Nov/Dec 2012) 15. Construct the PDA accepting the language {(ab) n/n≥1} by empty stack. (Nov/Dec 2012) 16. Construct the PDA for L={WWR/w is in (a+b)*} (May/June 2012) 17. Discuss the equivalence between PDA and CFG. (May/June 2012) 18. Is NPDA (Nondeterministic PDA) and DPDA (Deterministic PDA) equivalent? Illustrate with an example.(Nov/Dec 2011) 19. What are the different types of language accepted by a PDA and define them. Is it true that the language accepted by a PDA by these different types provides different languages? (Nov/Dec 2011) 20. Convert the grammar S->aSb/A, A->bSa/S/ϵ to a PDA that accepts the same language by empty stack. (Nov/Dec 2011) 21. What is deterministic PDA? Explain with an example.(Nov/Dec 2010) 22. Construct the PDA for the language L={wcw R / w is in (0+1)*} )(Nov/Dec 2010) 23. Let L is context free language. Prove that there exists a PDA that accepts L. (Nov/Dec 2010) 24. Construct a PDA equivalent to the following grammar. 25. S->aAA A->aS/bS/a. (Nov/Dec 2009) 26. Prove that every language recognized by a PDA is Context free.(Nov/Dec 2009) 27. Construct a PDA for the set of palindrome over the alphabet {a,b}. (Nov/Dec 2009) 28. Construct a Push Down Automata that will accept the language generated by the grammar G=({S,A}.{a,b},S,P) with the productions S->AA/a,A->SA/b. (May/June 2009) 29. Construct an NPDA that accept the language generated by the grammar 30. S->aSbb/abb. (May/June 2009) 31. Design a PDA for recognizing the language {ambncm,n,m≥ 1} using empty stack. 32. Construct an unrestricted PDA equivalent to the grammar given below: 33. S->aAA, A->aS/bS/a. 34. Construct a PDA for the language {anb2n/n ≥0}. (Nov/Dec 2008) 35. Constrcut PDA for the grammar 36. S->aB/bA A->a/aS/bAA B-b/bS/aBB

Year : 2015-16

UNIT-IV Turing Machines

Sem. : ODD

Subject Code

: CS6503

Branch

: CSE

Subject Name

: Theory of Computation

Year/Sem.

: III/V

PART-A

1. Define a Turing machine. (MAY-2014, NOV/DEC-2010, MAY/JUNE-2008) 2. List out the different techniques for Turing machine construction. (NOV/DEC-2013) 3. What are the applications of Turing Machine? (NOV/DEC-2012) 4. Design a TM that accepts the language of odd integers written in binary. (NOV/DEC2011) 5. Construct a Turing Machine to compute „n mod 2‟ where „n‟ is represented in the tape in unary form consisting of only 0‟s. (MAY/JUNE-2011) 6. Design a T.M with no more than 3 states that accepts L= {a(a+b)*}. Assume  = {a, b}. (MAY/JUNE-2010) 7. Construct a Turing Machine for zero function: f: N->N, f(x) =0. (MAY/JUNE-2009) 8. Differentiate multi tape and multi track Turing machines. (NOV/DEC-2008) 9. What is the minimum no. of stacks needed for simulating a TM using a multi-stack machine? (NOV-2008) 10. What is meant by multi tape Turing Machine? (NOV/DEC-2007) 11. What is the class of language for which the TM has both accepting and rejecting configuration? Can this be called a context free language? (NOV/DEC-2006) 12. The binary equivalent of a positive integer is stored in a tape. Write the necessary transitions to multiply that integer by 2. (NOV/DEC-2006) 13. Mention any two problems which can only be solved by TM. 14. List out different techniques for turing machine construction. 15. Design a turing machine with not more than three states that accepts the language a(a+b)*. Assume Σ={a,b} 16. Is it possible that a turing machine could be considered as a computer of functions from integers to integers? If yes, justify your answer. 17. Define multitape turing machine.(Nov/Dec 2014) 18. Describe the non-deterministic turing machine model. Is it true the non-deterministic turing machine model‟s are more powerful than the basic turing machines (In the sense of language acceptance)? 19. What is meant by halting problem? (MAY/JUNE-2008) 20. What are the Chomskian hierarchy of languages?

PART-B

1. Design a TM, M to implement the function “MULTIPLICATION” using the subroutine “COPY”. (Nov/Dec 2014) 2. Construct a TM to perform copy operation. (May/June 2015) 3. Design a Turing machine to accept the language L= {0 n1n|n>=1} and simulate its action on the input 0011. (MAY-2014) 4. Write short note on checking off symbols. (MAY-2014, MAY -2009) 5. Explain Turing machine as a computer of integer functions with an example. (NOV/DEC-2013) 6. Remove  productions from the given grammar. (NOV/DEC-2013) 7. Write short notes on the following: (NOV/DEC-2013)

(i) Two-way infinite tape TM. (ii) Multiple tracks TM. 8. Discuss about programming techniques for Turing machines.(MAY/JUNE-2013, NOV/DEC-2012) 9. Design a Turing Machine which reverses the given string {abb}. (NOV/DEC-2012) 10. Explain any two higher level techniques for Turing machine construction. (MAY/JUNE-2012) 11. Construct Turing machine for L = {  n  n  n|n>=  }. (MAY/JUNE-2012) 12. State the techniques for Turing Machine construction. Illustrate with a simple language. (NOV/DEC-2011) 13. Explain the different models of Turing Machines. (NOV/DEC-2011) 14. Construct the Turing Machine to accept the language: a nbncn. (MAY/JUNE-2011) 15. Construct a Turing Machine to perform proper subtraction. (MAY/JUNE-2011) 16. Construct the Turing Machine for the language L= {1 n0n|n>=1}. (NOV/DEC-2010) 17. Construct the Turing Machine for the language: L= {ww R | w is in (0+ 1)*}. (NOV/DEC2010)

18. Construct a Turing Machine to move an input string over the alphabet A = {a} to the right one cell. Assume that the tape head starts somewhere on a blank cell to the left of the input string. All other cells are blank, labeled by ^. The machine must move the entire string to the right one cell, leaving all remaining cells blank. (MAY/JUNE-2010) 19. Design a Turing Machine to recognize each of the following languages. (NOV/DEC2009) 1. {0n1n|n>=1} 2. {wwR|w (0+1)*} 20. Prove that the TM with one-way infinite tape and two-way infinite tape are equivalent. (NOV/DEC-2009) 21. Design a Turing Machine to compute n2. (NOV/DEC-2009) 22. Construct a Turing Machine M for a language L={a nbn|n>=1}. (MAY/JUNE-2009) 23. Design a deterministic Turing Machine to accept the language: L= {a ibici|i>=0}. (MAY/JUNE-2008) 24. Design a Turing Machine that computes x + y where x and y are positive integers. (MAY/JUNE-2007) 25. Design a Turing Machine M for f(x,y,z)=2(x+y)-z, z