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VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur-603203
DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING QUESTION BANK – ODD SEMESTER
Academic Year: 2016-17
Year & Semester : III / V
Section : CSE - 1 & 2
Subject Code : CS6503
Subject Name : Theory of Computation
Degree & Branch : B.E – C.S.E.
Staff in charge : Ms.Shanthi.S & Dr.A.Samydurai
S.No QUESTIONS COMPETENCE LEVEL
UNIT -1
PART - A
1. Differentiate between DFA and NFA. Understand BTL-2
2. List the operators of Regular Expressions Remember BTL-1
3. Define inductive proof. Remember BTL-1
4. What is a finite automata? Draw the Transitiondiagram and
Transition Table. Remember BTL-1
5. Differentiate between regular expression and regular language Analyze BTL-4
6. Tabulate the regular expression for the following
(i) L1=set of strings 0 and 1 ending in 00
(ii) L2=set of all strings 0 and 1 beginning with 0 and
ending with 1 Analyze BTL-4
7. Describe what is non-deterministic finite automata and the
applications of automata theory Remember BTL-1
8. Illustrate a regular expression for the set of strings over
{0,1}that have at least one Apply BTL-3
9. Define Language and Grammar with an example
Remember BTL-1
10. Describe an identifier with a transition diagram (automata)
Understand BTL-2
11. Define ε-NFA.
Remember BTL-1
12. Summarize minimization of DFA Evaluate BTL-5
13. Discuss the notation of DFA Understand BTL-2
14. Illustrate if L be a set accepted by an NFA then there exists a
DFA that accepts L Apply BTL-3
15. Explain a finite automaton for the regular expression 0*1*. Evaluate BTL-5
16. Develop a pumping lemma for regular set and what are the
applications of pumping Lemma Create BTL-6
17. Explain L={0
n1
2n/n>=1}is not regular
Analyze BTL-4
19. Illustrate a regular expression for the set of all the strings
have odd number of 1‟s
R.E=1(0+11)* Apply BTL-3
20. Compose the difference between the + closure and * closure Create BTL-6
PART - B
1.
i) Explainif L is accepted by an NFA with ε-transition then
show that L is accepted by an NFA without ε-transition (8)
ii) Construct a DFA equivalent to the NFA.
M=({p,q,r},{0,1},δ,p,{q,s}) Where δ is defined in the
following table.(8)
0 1 p {q,s} {q} q {r} {q,r} r {s} {p} s - {p}
Evaluate BTL-5
2.
i) Demonstrate how thesetL= {abn/n>=1} is not a regular.
(6)
ii) Construct a DFA equivalent to the NFAgiven below:
(10)
0 1
p {p,q} P
q r R
r s -
s s S Apply
BTL-3
3.
(i) Examine whetherthe language=(0n1n/ n>=1)is regularor
not?Justifyyour answer. (6)
(ii) Let L be a set accepted by a NFA then show that there
exists a DFA that accepts L(0)
Remember BTL-1
4.
(i) Summarize a construction of NDFA accepting all string in
{a,b}with either two consecutive “a sort two consecutive
b‟s(8)
(ii) Give the DFA accepting the following language. Set of all
strings beginning with a 1 that when interpreted as a binary
integer is a Multiple of 5.(8)
Understand BTL-2
5. (i) Describethe following: Let L be a set accepted by an Understand BTL-2
NFA. Then prove that there exists a deterministic finite
automaton that accepts L. Is the conversetrue?Justifyyour
answer.(6)
(ii) Construct DFA equivalent to the NFA given below: (8)
6.
(i) Compose that a language L is accepted by some ε–
NFA if and only if L is accepted by some DFA. (6) (ii) Consider the following ε–NFA. Compute the ε–closure of
each state and find it‟s equivalent DFA. (8)
ε A b C
p
{q {p
Ф
Ф
q
{r
ф
{q
Ф
*r Ф ф ф {r}
Create BTL-6
7.
i) Classify how a language L is accepted by some DFA if L is
accepted by some NFA (6)
(ii) Convert the following NFA to its equivalent DFA.(10)
0 1
p {p,q} {p}
q {r} {r}
r {s} ф
*s {s} {s}
Apply BTL-3
8.
(i) Describe that “A language L is accepted by some DFA if
and only if L is accepted by some NFA(8)
(ii) Construct Finite Automate equivalent to the regular
expression (ab+a)*(8)
Remember BTL-1
9
(i) Describe the construction of NFA with ε-transition from any given regular expression. (6) b) Let A= (Q,∑, δ,q0 ,{qf)be a DFA and suppose that for all a in ∑we have δ(q0,a)=δ(qf, a). Show that if xis a non-empty
Remember BTL-1
string in L(A),then for all k>0,xkis also in L(A).(10)
10.
(i) Point out the steps in conversion of NFA to DFA and for
the following convert NFA to aDFA (8)
(ii)Discuss on the relation between DFA and minimal DFA(8)
Analyze BTL-4
11.
(i) Tabulate the difference between the NFA and DFA (6)
(ii) Convert the following ε-NFA to DFA(10)
states ε a b C
p Ф {p} {q} {r}
q {p} {q} {r} Ф
*r {q} {r} ф {p}
Remember BTL-1
12.
(i) Describe the extended transition function for NFA, DFA
and ε-NFA. Consider the following ε-NFA for an identifier.
Consider the ε-closure of each state and find it‟s equivalent
DFA(10)
(ii) State the pumping lemma for the regular languages. show
that the set L={0i2
|i>=1}not regular (6)
Understand BTL-2
13. (i) Analyze and Construct a minimized DFA from the regular
expression (x+y)x(x+y)*.Trace for string w=xxyx (8) Analyze BTL-4
1 2 3 4
5 6
8 9
7 1
0
(ii) Using Pumping Lemma for the regular sets ,prove that the
language ]L={a m
bn|m>n} is not regular(8)
14.
(i) Analyze and Prove that if n is a positive integer such that n
mod 4 is 2 or 3 then n is not a perfect square. (8)
(ii) Construct a DFA that accept the following language
{x€{a,b}:|x|n =odd and :|x|b=even (8)
Analyze BTL-4
UNIT -1I
PART - A
1
Examine the string aaabbabbba for the Grammar G with
S- aB|bA
A a|aS|bAA
B b|bS|aBB Remember BTL-1
2 Defineambiguous grammar and CFG. Remember BTL-1
3 Inferthe set of strings over the alphabet {O} of the
form0nwhere n is not a prime is regular? Prove or disprove
Analyze BTL-4
4 GiveaCFG forthelanguageof palindromestringover {a,b}.Write theCFG forthe language,L=(anbn|≥n) Understand BTL-2
5 Examinethe context free Grammar representing the set of
Palindrome over (0+1)* Remember BTL-1
6 Define parse tree and derivation. Remember BTL-1
7 Demonstratethe grammar is ambiguous
S SS|(S)|S(S)S|E Apply BTL-3
8 Point outthe various types of grammar with example . Analyze BTL-4
9 DiscussL(G)whereG=({S},{0,1},{S->0S1,S->ε},S) Understand BTL-2
10 Describe that id+ id*id can begenerated bytwo distinct leftmost and right most derivation in the grammar E->E+E|E*E| (E)|id
Understand BTL-2
11 Differentiate null production and unitproduction Understand BTL-2
12 Concludethe procedure for converting CNF to GNF with an
example.
Evaluate BTL-5
13 Definethe two normalforms of CFG. Remember BTL-1
14 Compareno useless symbol and NULL production. Analyze BTL-4
15 Illustratesententialforms with an example. Apply BTL-3
16
Show 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 Apply BTL-3
17
Conclude CFG without null production from:
S a|Ab|aBa
A b|ε
B b|A Evaluate BTL-5
18 Convince your answer of acontext freeGrammar for
thegivenexpression (a+b) (a+b+0+1)* Create BTL-6
19 List the three ways to simplify a context free grammar? What
are the properties of the CFL generated by a CFG? Remember BTL-1
20 DefineGNF and CNF Create BTL-6
PART B
1
(i)Explain and draw the parse tree for the string 1+2*3 given the grammar G=(V, ,R,E)where V={E,D,1,2,3,4,5,6,7,9,0,+,-,*,/,9,)} ={1,2,3,4,5,6,7,8,9,0,+,-,*,/,(,)} where R contains the following rules : E D|(E)|E+E|E-E|E/E D 0|1|2|…9 (8) (ii)Let G=(V,T,P,S) be a Context Free Grammar then prove that if the recursive inference procedure calls tells us that terminal string W is in the language of variable A ,then there is a parse tree with a root A and yield w(8)
Evaluate BTL-5
2
(i)Define Leftmost derivation Let G be a CFG and let Aw .Design a left most derivation of w(8) (ii) Let G be the grammar s0B|1A, A0|0S|1AA, B1|1S|0BB .For the string 00110101, find its leftmost derivation and derivation tree. (8)
Remember BTL-1
3
(i)If G is grammar SSbS|a, expressthat G is ambiguous. (8) (ii)Show that the grammar Sa|abSb|aAb
AbS|aAAb is ambiguous. (8) Understand BTL-2
4
(i)Describe that the following grammars are ambiguous
S aSbS/bSaS/ ε
S AB/aaB,
A a/Aa,
B b (8) ii)If SaSb|aAb, AbSa Aba is the context free grammar. Give the context free
language. (8)
Remember BTL1
5
(i)By Considering the grammar
Remember
BTL1
EE + E | E*E | (E) | I
I a+b Describe that the grammar is ambiguous and remove the ambiguity. (8) (ii) Discuss in detail about ambiguous grammar and removing
ambiguity from grammar(8)
6
i) Solve the following grammar
S aAa | bBb | BB
A C
B S | A
C S | ε for the string abaaba .Give
a) Left most derivation(4)
b)Right most derivation(4)
c)Derivation Tree(4) d) For the string abaabbba, find the right most derivation. (4) Apply BTL-3
7
(i)Let G=(V,T,P,S)be a context free grammar (CFG).Then Sαif and only if there is a derivation tree for G which yields α.Illustrate the relationship between Derivation and Derivation Trees(8) (ii)Consider the productions: SaB|bA AaS|bAA|a BbS|aBB|b For the string aaabbabbba ,find the leftmost derivation(8)
Apply BTL-3
8
(i)If SaSb|aAb, AbSa Aba is the context free grammar. Analyzethe context free language(8)
(ii)Consider the grammar
EE + E | E*E | (E) | I
I a+b Show that the grammar is ambiguous and remove the ambiguity (8) Analyze BTL-4
9
(i)Give the formal pushdown automata that accepts {wcwR|w
in (0+1)} (8) ii)Convert the following grammar into GNF (8) S XY1/0 x 00X/Y Y 1X1
Understand BTL-2
10
(i)Develop an equivalent grammar G in CNF for the grammar G1 where
G1=({S,A,B},{a,b},{S A SB| ε , A aAS|a,B SbS|A|bb},S)(8)
(i) What is an ambigous grammar ?Explain with an example. (8)
Create BTl-6
11
Examine the grammar S 0A0/1B1/BB B C B S/A C S/ ε and Simplify using the safe order
(1) Eliminate ε- productions (4) (2) Eliminate unit production(4) (3) Eliminate useless symbols(4) (4) Put ( resultant) the grammar in Chomsky normal
form(4)
Remember BTL-1
12
(i)Give the Chomsky normal form equivalent to the grammar SAB|aB, AbAA|aSa|a BaBB|bS|b(8) (ii) Convert the grammar SAB ABS|b BSA|a into GNF(8)
Understand BTL 2
13
(i)Analyze that For every CFG; there is an equivalent grammar in CNF. (8) (ii)Find a Grammar in CNF equivalent to (8) SaAbB AaA|a BbB| ε
Analyze BTL-4
14.
(i)Define GNF. Compare GNF and CNF. (8)
(ii)Every CGL L can be generated by a CFG G in GNF
Construct a grammar in GNf equivalent to
P={SaSa, S bSb, S aa, S bb}(8)
Analyze BTL-4
UNIT - III
PART A
1. What are the different ways of languages accepted by PDA and
define them? BTL 2 Understa
nd
2.
Summarize PDA .Convert the following CFG to PDA
S aAA , A aS|bS|a.
BTL 2 Understa
nd
3. Define the pumping Lemma for CFLs BTL 1 Rememb
er
4. List the main application of pumping Lemma in CFL’s BTL 1 Rememb
er
5. Draw an example for PDA BTL 2 Understa
nd
6.
Compare Deterministic and Non deterministic PDA. Is it true that non deterministic PDA is more powerful than that of deterministic PDA? Justify your answer
BTL 2 Understa
nd
7. What is pushdown automaton? BTL 1 Rememb
er
8.
Use the CFL pumping lemma to show how each of these languages not to be context-free
{aibjck| i<j<k}
BTL 5 Evaluate
9. Describe the acceptance of a PDA with empty stack BTL 1 Rememb
er
10. Design equivalence of PDA and CFG BTL 6 Create
11.
Point out the languages generated by a PDA using final state of
the PDA and empty stack of that PDA
BTL 4 Analyze
12. Illustrate the rule for construction of CFG from given PDA BTL 3 Apply
13. Design a PDA for accepting a language{ L=anbn|n>=1} BTL 5 Evaluate
14. What is Instantaneous Descriptions ( ID )? BTL 1 Rememb
er
15.
Construct the languages generated by a PDA using final state
of the PDA and empty stack of that PDA.
BTL 3 Apply
16.
What is the language generated by a PDA using the two
methods of accepting a language?
BTL 4 Analyze
17.
What is additional feature PDA has when compared with NFA?
Is PDA superior over NFA in the sense of language acceptance?
Justify your answer.
BTL 1 Rememb
er
18.
Illustrate what actions take place in the PDA by the transitions
(moves)
δ(q,a,Z)={(p1,γ1),(p2, γ2),…..(pm, γm)} and
δ(q, ε,Z)={(p1,γ1),(p2, γ2),…..(pm,γm)}.
BTL 3 Apply
What are the different ways in which a PDA accepts the
language?
19. Point out the additional features a PDA has when compared with
NFA
BTL 4 Analyze
20. Formulate the acceptance by final state and by empty stack in PDA
BTL6 Create
PART - B
1.
(i)Discuss about PDA and CFL Prove the equivalence of PDA
and CFL.(8)
(ii)If L is Context free language then prove that there exists
PDA M such that L=N(M). .(8)
BTL 2 Understa
nd
2.
(i)Describe the different types of acceptance of a PDA. Are they
equivalent in sense of language acceptance? Justify your
answer.(8)
(ii)Design a PDA to accept {0n1
n|n>1} Draw the transition
diagram for the PDA. Show by instantaneous description that
the PDA accepts the string „0011‟.(8)
BTL 1
Rememb
er
3.
(i)Define deterministic PDA‟s? Give example for Non –
deterministic and Deterministic PDA.(8)
(ii)Construct a PDA accepting {an b
m a
n / m, n>=1} by empty
stack. Also construct the corresponding context-free grammar
accepting the same set.(8)
BTL 1 Rememb
er
4.
(i)State the Pumping Lemma for CFL and Develop the
language L={ an b
n c
n / n>=1}(8)
(ii)Prove that L is L(M2 ) for some PDA M2 if and only if L is N(M1) for some PDA M(8)
BTL 6
Create
5.
(i)Define Non Deterministic Push Down Automata. Is it true that DPDA and NDPDA are equivalent in the sense of language acceptance is concern? Justify Your answer.(8) (ii)Convert PDA to CFG.PDA is given by P=({p,q},{0,1},{X,Y},δ,q,Z}, δ is defined by δ(p,1,z)={(p,XZ)}, δ(p,ε,Z)={p, ε)}, δ(p,1,X)={(p,XX)}, δ(q,1,X)={(q, ε)}, δ(p,0,X)={(q,X0}
BTL 1 Rememb
er
δ(q,0,Z)={(p,Z)} (8)
6.
(i)Define PDA. Give an Example for a language accepted
byPDA by empty stack. (8)
(ii)Convert the grammar
S 0S1|A
A 1A0|S| εinto PDA that accepts the same language by the
empty stack .Check whether 0101 belongs to N(M) (8)
BTL 2 Understa
nd
7.
(i)Analyze the theorem: If L is Context free language then prove
that there exists PDA M such that L=N (M). (8) (ii) Prove that if there is PDA that accepts by the final state then there exists an equivalent PDA that accepts by Null State.(8)
BTL 4 Analyze
8.
(i)Recommend. Explain different types of acceptance of a PDA.
Are they equivalent in sense of languageacceptance? Justify
your answer (8) (ii)Show that the language is not context free{0i1j|j=i2} (8)
BTL 5 Evaluatin
g
9.
(i)Examine Construct the grammar for the following PDAM.
M=({q0, q1},{0,1},{X,z0},δ,q0,Z0,Φ) and where δis given by
δ(q0,0,z0)={(q0,XZ0)},δ(q0,0,X)={(q0,XX)},δ(q0,1,X)={(q1,
ε)},δ(q1,1,X)={(q1, ε)},δ(q1, ε,X)={(q1, ε)},
δ(q1, ε, Z0 )={(q1, ε)}. (8)
(ii)Prove that if L is N(M1) for some PDA M1 then L is L(M2 )
for some PDA M2. (8)
BTL 3 Applying
10.
(i)Analyze a PDA that recognizes the language
{ai b
j c
k | i,j,k>0 and i=j or i=k}. (8)
(ii)Discuss about PDA acceptance
1) From empty Stack to final state. 2)From Final state to
Empty Stack
BTL 4
Analyze
11.
Examine and construct a CFG G which accepts N(M), where
M=({q0, q1},{a,b},{z0,z},δ,q0,z0,Φ) and where δis given by
δ(q0,b,z0)={(q0,zz0)}
δ(q0, ε,z0)={(q0, ε)}
δ(q0,b,z)={(q0,zz)}
δ(q0,a,z)={(q1,z)}
δ(q1,b,z)={(q1,ε)
δ(q1,a,z0)={(q0,z0)} Show that anbncn is not context free language i.e. show that the set
of strings of a’ s and b’s and c’s with an equal number of each is
not context free (16)
BTL-1 Rememb
er
12.
(i)Give PDA to accept the language
L= {a n b n|n>=1}by empty stack and by final stack.
(ii)Construct PDA accepting L={anb3n|n>=1}by empty store
BTL-2 Understa
nd
13.
(i)Show the PDA accepting the language {(ab)n |n>1} by empty
stack (8)
(ii)Construct a Transition table for PDA which accepts the
language L={a2nbn|n>+1}(8)
BTL-3 Apply
14. (i)Explain and Prove Pumping Lemma for CFL(8)
(ii)If L=N(PN)for some PDA PN =(Q,∑,┌,δ,N,qo,Zo) then there is
aPDA PF such that L=L(pF)[From empty stack to final stack](8)
BTL-4 Analyze
UNIT- IV
PART A
1. What is multitape Turing machine? Explain in one move. What
are the actions take place in TM?
BTL 2 Understa
nd
2. What is the Basic Turing Machine model and explain in one
move? What are the actions take place in TM?
BTL 3 Apply
3.
Canyou describe the non-deterministic Turing Machine model.
Is it true the non-deterministic Turing Machine models are more
powerful than the basic Turing Machines? (In thesense of
language Acceptance
BTL 1 Rememb
er
4. List out the hierarchy summarized in the Chomsky hierarchy BTL 4 Analyze
5. What is meant by a Turing Machine with two way infinite tape? BTL1 Rememb
er
6. Define Turing Machine. BTL1 Rememb
er
7. What are the applications of Turing machine? BTL 2 Understa
nd
8. Define LBA. BTL 1 Rememb
er
9. What is the class of language for which the TM has both
accepting and rejecting configuration? Can this be called a
Context free Language.
BTL 2 Understa
nd
10.
Show a TM that accepts the language of odd integers written in
binary.
BTL 3 Apply
11. What are the special features of TM?Define universal Tm .Define Instantaneous description of TM
BTL 5 Evaluate
12. Define two way infinite Tape TM. BTL 1 Rememb
er
13. Prepare the difference between multi head and multi tape Turing
machine BTL 6 Create
14. Explain what is the class of language for which the TM has both
accepting and rejecting configuration? Can this be called a
Context free Language
BTL 5 Evaluate
15. Draw a transition diagram for a Turing machine to compute n mod 2.
BTL 1 Rememb
er
16. What are the techniques for TM construction? BTL 2 Understa
nd
17. Design how a Turing Machine can be regarded as a computing
device to compute integer functions
BTL 6 Create
18. Differentiate TM and PDA BTL 4 Analyze
19. What is the role of checking off symbols in a Turing Machine? BTL 4 Analyze
20. What Halting Problem? BTL 3 Apply
PART - B
1.
(i)State and describe the Halting Problem for Turing machine(8)
(ii)Design a Turing Machine to accept the language
L={0n
1n /n>=1} Draw the transition diagram (also specify the
instantaneous description to trace the string 0011(8)
BTL 1 Remember
2.
(i)Describe the Chomsky hierarchy of languages (8)
(ii)Explain the programming techniques for the TM construction.(8)
BTL 2 Understand
3.
(i)Discuss TM to accept the language LE={1n 2
n 3
n | n >= 1 }
(8)
(ii)Explain in detail about programming techniques of the TM(8)
BTL 2 Understand
4.
(i)Illustrate the Turing machine for computing f(m, n)=m-n
(proper subtraction). (8)
(ii)Design a Turing Machine to compute f(m+n)=m+n, V
m,n>=0 and simulate their action on the input 0100. (8)
BTL 3 Apply
5. (i)Examine is the role of checking off symbols in a Turing
Machine (8)
BTL 1 Remember
(ii)Design a Turing Machine M to implement the function
“multiplication” using the subroutine copy (8)
6.
(i)Demonstrate in in detail about Multitape TM with an example (8)
(ii)Prove that if a language is accepted by a multitape Turing machine ,it is accepted by a single-tape TM (8)
BTL 3 Apply
7.
(i)Summarize in detail about Multihead and multitape TM with an
example.(8)
(ii)Construct a Turing Machine that recognizes the language
{wcw / w € {a, b} + } (8)
BTL 5 Evaluate
8. (i)Explain the TM as computer of integer function with an
example (8)
(ii)Design a TM to implement the function f(x)= x+1. (8)
BTL 4 Analyze
9.
(i)Design a TM to accept the set of all strings {0,1} with 010 as substring.(8)
(ii)Write shot notes on Two –way infinite tape TM.(8)
BTL 6 Create
10.
(i)Describe computing a partial function with a TM (8)
(ii)Design a TM to accept the language LE={an bn cn | n > 1 }
(8)
BTL 1
Remember
11.
(i)Define Turing machine for computing f(m, n)=m*n,n€N(8)
(ii)Write notes on Partial solvability .(8)
BTL -1 Remember
12.
(i)Discuss in detail about Multiple tracks TM (8)
(ii)Design a Tm which reverses the given string {abb}.(8)
BTL 2 Understand
13.
(i)Analyze and Construct a TM to compute a function f(w) =W
R where W€{a,b} (8)
(ii)Design a TM to accept the set of all strings {0,1} with 010 as substring (8)
BTL 4 Analyze
14.
(i)Explain in detail about Chomsky hierarchy of languages (8)
(ii)Design a TM with no more than three states that accepts the language. a(a+b) *.Assume €={a,b} (8)
BTL 4 Analyze
UNIT - V
PART –A
1. Distinguish between PCP and MPCP? What are the concepts used
in UTMs?
BTL 2 Understand
2. Define the language NSA and SA. BTL 1 Remember
3. When a recursively enumerable language is said to be recursive? BTL 2 Understand
4. Compare and contrast recursive and recursively enumerable languages.
BTL 4 Analyze
5. State when a problem is said to be decidable and give an example of an undecidable problem.
BTL 1 Remember
6. Whatis auniversal language Lu? BTL 1 Remember
7.
Is it true that the language accepted by a non-deterministic
Turing Machine is different from recursively enumerable
language?
BTL 5 Evaluate
8. Give two properties of recursively enumerable sets which are undecidable
BTL 6 Create
9. When we say a problem is decidable? Give an example of undecidable problem.
BTL 4 Analyze
10. What are (a) recursively enumerable languages (b) recursive sets? BTL 6 Create
11. Define the classes of P and NP. BTL 1 Remember
12. Is it true that complement of a recursive language is recursive? Justify your answer
BTL 2 Understan
d
13. Give an example for an undecidable problem BTL 1 Remember
14. Compare the three ways to improve MTTF. BTL 4 Analyze
15. Define Primitive Recursive Function BTL 3 Apply
16. Write the Properties of Recursive Languages. BTL 3 Apply
17. When a language is said to be recursively enumerable? BTL 5 Evaluate
18.
Prove that “If P1 and P2 are primitive recursive n-place predicates ,then so are the predicates p1 or p2 ,p1 and p2 ,and not p1
BTL 2 Understan
d
19. Define Time and space complexity of TM. BTL 3 Apply
20.
Distinguish between PCP and MPCP. What are the concepts used
in UTMs?
BTL 2 Understan
d
PART - B
1.
(i)Describe about the tractable and intractable problems.(8)
(ii)Prove that “MPCP reduce to PCP”(8)
BTL 1 Remember
2.
(i)Describe about Recursive and Recursive Enumerable languages
with example.(8)
(ii)State and explain RICE theorem.(8)
BTL 1 Remember
3.
(i)Summarize diagonalization language.(8)
(ii) Show that the language Ld is not recursive enumerable
language(8)
BTL 2 Understan
d
4.
(i)Discuss post correspondence problem .Let ∑={0,1}.Let A and B be the lists of three strings each ,defined as
Does the PCP have a solution?(10) (ii)Prove that the universal language is recursively enumerable.(6)
List A List B
i wi xi
1 1 111
2 10111 10
3 10 0
BTL 2 Understan
d
5. (i)Explain computable functions with suitable example.(8)
(ii)Explain in detail notes on Unsolvable Problems(8)
BTL 4 Apply
6. (i)Describe in detail notes on universal Turing machines with
example(8)
(ii)Write short notes NP-complete problems(8)
BTL 1 Remember
7. Show that the language L and its complement L‟ are both recursively enumerable then L is recursive (16)
BTL 3 Apply
8.
(i)Conclude problem p2 cannot be solved in polynomial time can be proved by the reduction of a problem p1, which is under class p1
to p2.(8)
(ii)Write short notes on PCP(8)
BTL 5 Evaluate
9. Explain Universal Turing machine and shoe that the universal
language is recursively enumerable but not recursive.(16)
BTL 6 Create
10.
(i)Prepare the recursively Enumerable Language with example.
(ii)Show that the following problem is undecidable. Giventwo
CFGs G1 and G2 is L(G1) L(G2) =∅ (8+8)
BTL 4 Analyze
11.
(i)Show that the characteristic function of the set of all even
numbers is recursive (8)
(ii)Explain in detail notes on primitive recursive functions with
examples(8)
BTL-3 Apply
12. (i)Point out the Measuring and Classifying Complexity(8)
(ii)Does PCP with two lists x=(b,b ab3,ba) and y=(b
3,ba,a) have
a solution(8)
BTL-4
13.
(i)Describe in detail Time and Space Computing of a Turing
Machine(8)
(ii)Show that it is undecidable for arbitrary CFG „S G1 and G2
whether L (G1) L(G2) is aCFL.(8)
BTL-2 Understan
d
14.
(i)Explain in detail Polynomial Time reduction and NP-
completeness.(8)
(ii)Write short notes on NP-Hard Problems.(8)
BTL 1 Remembe
r