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Transcript of QVIII
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MATCH ITEMS
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Match the following:-
Q1.A (00)* 1 Set of all 0s
B 0(00)* 2 Set of alleven numberof 0s
C 00(00)*+0(00)* 3 Set of all oddnumber of0s
D 0* 4 Set of all 0s
excluding 5 Set of all 0s
which aremultiples ofthree andfour
6 Set of all 0swhich aremultiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
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(iv) A->2,B->3,C->4,D->1
Q2.
A (00)*(11)* 1 Set of allstrings over{0,1} notcontaining a1
B 0(00)*(11)* 2 Set of alleven numberof 0sfollowed byan evennumber of1s
C 00(00)*+0(00)* 3 Set of all odd
number of0s followedby an evnnumber of1s
D 0* 4 Set of all 0s
excluding 5 Set of all 0swhich are
multiples ofthree andfour
6 Set of all 0s
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which aremultiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q3.
A (0+10)*(+1) 1 Set of allstrings over
{0,1} notcontainingtwoconsecutive0s
B 0(00)* 2 Set of allstrings over
{0,1} notcontainingtwoconsecutive1s
C 00(00)*+0(00)* 3 Set of all odd
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number of0s
D (1+01)*(+0) 4 Set of all 0sexcluding
5 Set of all 0swhich aremultiples ofthree andfour
6 Set of all 0swhich aremultiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q4.A (0+10)*(+1) 1 Set of allstrings over{0,1} notcontainingtwo
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consecutive0s
B (0+10+110)*(+1+11) 2 Set of allstrings over{0,1} notcontainingtwoconsecutive1s
C (1+01+001)*(+0+00) 3 Set of allstrings over
{0,1} notcontainingthreeconsecutive1s.
D (1+01)*(+0) 4 Set of allstrings
over{0,1}notcontainingthreeconsecutive0s.
5 Set of all 0s
which aremultiples ofthree andfour
6 Set of all 0swhich are
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multiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q5.
A (0+10)*(+1) 1 Set of allstrings over{0,1} not
containingtwoconsecutive0s
B (0+10+110)*(+1+11) 2 Set of allstrings over{0,1} not
containingtwoconsecutive1s
C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of allstrings over
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{0,1} notcontainingthree
consecutive1s.
D (1+01)*(+0) 4 Set of allstrings over{0,1}containingan evennumber of
0s and anevennumber of1s.
5 Set of all0s whichare
multiples ofthree andfour
6 Set of all0s whicharemultiples of
three
Answer:
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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q6.
A (11+0)*(00+1)* 1 Set of allstrings over{0,1} not
containingtwoconsecutive0s
B (0+10+110)*(+1+11) 2 Set of allstrings over{0,1}where
in somehead of thestring the1s occur inconsecutivepairs andin the tail
of thestring the0s occur inconsecutivepairs
C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of all
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strings over{0,1} notcontaining
threeconsecutive1s.
D (1+01)*(+0) 4 Set of allstrings over{0,1}containingan even
number of0s and anevennumber of1s.
5 Set of all0s which
aremultiples ofthree andfour
6 Set of all0s whichare
multiples ofthree
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q7.
A (11+0)*(00+1)* 1 Set of allstrings over
{0,1} notcontaining twoconsecutive 0s
B (01+10)* 2 Set of allstrings over{0,1}where insome head of
the string the1s occur inconsecutivepairs and inthe tail of thestring the 0soccur in
consecutivepairs
C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of allstrings over{0,1}containingan equal
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number of 0sand 1s whereevery prefix
has at mostone more 0than 1s or atmost one more1 than 0s.
D (1+01)*(+0) 4 Set of allstrings over{0,1}
containing aneven numberof 0s and aneven numberof 1s.
5 Set of all 0swhich are
multiples ofthree and four
6 Set of all 0swhich aremultiples ofthree
Answer:
(i) A1,B->2,C->3,D->4
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(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q8.
A (11+0)*(00+1)* 1 Set of allstrings over{0,1} ending in00.
B (01+10)* 2 Set of allstrings over{0,1}where insome head ofthe string the1s occur inconsecutivepairs and in
the tail of thestring the 0soccur inconsecutivepairs
C [00+11+(01+10)(00+11)*(01+10)]* 3 Set of allstrings over
{0,1}containingan equalnumber of 0sand 1s whereevery prefixhas at most
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one more 0than 1s or atmost one more
1 than 0s.D (0+1)*00 4 Set of allstrings over{0,1}containing aneven numberof 0s and aneven number
of 1s.5 Set of all 0s
which aremultiples ofthree and four
6 Set of all 0swhich are
multiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
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Q9.
A (11+0)*(00+1)* 1 Set of allstrings over{0,1} notcontaining twoconsecutive 0s
B (01+10)* 2 Set of allstrings over
{0,1}where insome head ofthe string the1s occur inconsecutivepairs and inthe tail of thestring the 0s
occur inconsecutivepairs
C (0+1)*000(0+1)* 3 Set of allstrings over{0,1}containingan equal
number of 0sand 1s whereevery prefixhas at mostone more 0
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than 1s or atmost one more1 than 0s.
D (1+01)*(+0) 4 Set of allstrings over{0,1}containingthreeconsecutive0s.
5 Set of all 0s
which aremultiples ofthree and four
6 Set of all 0swhich aremultiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q10.
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A (11+0)*(00+1)* 1 Set of allstrings over{0,1} where
every pair ofconsecutive 0soccurs beforeany pair ofadjacent 1s.
B (01+10)* 2 Set of allstrings over{0,1}where in
some head ofthe string the1s occur inconsecutivepairs and inthe tail of thestring the 0s
occur inconsecutivepairs
C (0+1)*000(0+1)* 3 Set of allstrings over{0,1}containingan equal
number of 0sand 1s whereevery prefixhas at mostone more 0than 1s or at
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most one more1 than 0s.
D (0+10)*(1+10)* 4 Set of all
strings over{0,1}containingthreeconsecutive0s.
5 Set of all 0swhich are
multiples ofthree and four
6 Set of all 0swhich aremultiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q11.
A L=(0+1)*00(0+1)*00(0+1)* 1 Set of all
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Intersection(0+1)*11(0+1)*11(0+1)*consider the complement of
L
strings over{0,1} whereevery pair of
consecutive 0soccurs beforeany pair ofadjacent 1s.
B (01+10)* 2 Set of allstrings over{0,1}containingat most one
pair ofconsecutive 0sand at mostone pair ofconsecutive1s.
C (0+1)*000(0+1)* 3 Set of all
strings over{0,1}containingan equalnumber of 0sand 1s whereevery prefixhas at most
one more 0than 1s or atmost one more1 than 0s.
D (0+10)*(1+10)* 4 Set of allstrings over
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{0,1}containingthree
consecutive0s.
5 Set of all 0swhich aremultiples ofthree and four
6 Set of all 0swhich are
multiples ofthree
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q12.
A 0*(10*)* 1 Set of all strings over{0,1} where every pairof consecutive 0soccurs before any
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pair of adjacent 1s.
B (01+10)* 2 1*(01*)*
C The complement
of(0+1)*000(0+1)*
3 Set of all strings over
{0,1}containing anequal number of 0sand 1s where everyprefix has at mostone more 0 than 1sor at most one more 1than 0s.
D (0+10)*(1+10)* 4 (1+01+001)*(+0+00) 5 Set of all 0s which
are multiples of threeand four
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q13.
A 0*(10*)* 1 (Ra)* R
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B (01+10)* 2 1*(01*)*
C The complementof
(0+1)*000(0+1)*
3 Set of all strings over{0,1}containing an
equal number of 0sand 1s where everyprefix has at mostone more 0 than 1sor at most one more 1than 0s.
D R (aR)* where aand R are some
regularexpressions
4 (1+01+001)*(+0+00)
5 Set of all 0s whichare multiples of threeand four
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q14.
A 0*(10*)* 1 (Ra)* R
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B (r*s*)**** 2 1*(01*)*
C The complementof
(0+1)*000(0+1)*
3 (r+s)*
D R (aR)* where aand R are someregularexpressions
4 (1+01+001)*(+0+00)
5 Set of all 0s whichare multiples of threeand four
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q15.A 0*(10*)* 1 (Ra)* R
B (r*s*)**** 2 1*(01*)*
C (+R)* 3 (r+s)*D R (aR)* 4 R*
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where a andR are someregular
expressions 5 Set of all 0swhich aremultiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q16.
A (R*+S*)*RR 1 (Ra)* R
B (r*s*)**** 2 (R+S)*RRC (+R)* 3 (r+s)*D R (aR)*
where a andR are someregular
4 R*
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expressions
5 Set of all 0swhich are
multiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q17.
A (R*+S*)*RR 1 (Ra)* R
B (R+R+R+R)R 2 (R+S)*RR
C (+R)* 3 RRD R (aR)*
where a and
R are someregularexpressions
4 R
5 Set of all 0swhich are
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multiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q18.
A R(S+T) 1 (Ra)* RB (R+R+R+R)R 2 (RS+RT)
C (+R)* 3 RRD R (aR)*
where a andR are someregular
expressions
4 R
5 Set of all 0swhich aremultiples ofthree andfour
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6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q19.
A R(S+T) 1 RT+ST
B (R+R+R+R) 2 RS+RT
C (+R)*R 3 RD (R+S)T 4 RR
5 Set of all 0swhich aremultiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4
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(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q20.
A R(S+T) 1 RT+ST
B (R+R+R+R) 2 RS+RT
C R+S 3 R
D (R+S)T 4 S+R
5 Set of all 0swhich aremultiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q21.
A R(S+T)T 1 RT+ST
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B (R+S)+T 2 RST+RTT
C R+S 3 (R+S)+T
D (R+S)T 4 S+R
5 Set of all 0swhich aremultiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q22.
A R(S+T)T 1 RT+ST
B (R+S)+T 2 RST+RTT
C R+S 3 (R+S)+T
D (R+S)T 4 S+R5 Set of all 0s
which aremultiples ofthree and
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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q24.
A * 1 RT+STB (R+S)+T 2 C (RS)T 3 (R+S)+T
D (R+S)T 4 (RS)T
5 Set of all 0swhich aremultiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q25.
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A * 1 B (R+S)+T 2 C (RS)T 3 (R+S)+T
D * 4 (RS)T5 Set of all 0s
which aremultiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q26.
A * 1 B (R+S)+T 2 C R(ST) 3 (R+S)+TD * 4 (RS)T
5 Set of all 0swhich aremultiples of
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three andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q27.
A * 1 B (R+S)+T 2 C (00)*(1+01) 3 (R+S)+TD * 4 0*1
5 Set of all 0swhich aremultiples ofthree andfour
6 (000)*
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q28.
A * 1 B ((0+1)(0+1)(0+1))*+((0+1)(0+1)(0+1)(0+1))* 2 C (RS)T 3 Set of all
stringsover{0,1}whicharemultiples
of threeor four
D * 4 (RS)T5 Set of all
0swhichare
multiplesof threeand four
6 Set of allstrings
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over{0,1}which
aremultiplesof threeand four
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q29.
A * 1 B ((0+1)(0+1)(0+1))*+((0+1)(0+1)(0+1)(0+1))* 2 C
Consider the set accepted by the finiteautomata
3 Set of allstringsover
{0,1}whicharemultiplesof threeor four
a
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D
Consider the set accepted by the finiteautomata
4 +a
5 Set of all
0swhicharemultiplesof threeand four
6 Set of all
stringsover{0,1}whicharemultiplesof three
and four
Answer:
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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q30.
A Consider the setaccepted by thefinite automata,
M=({q},{0,1},,{q})(q,0)=q,(q,1)=q
1
B Consider the setaccepted by thefinite automata,
M=({q},{0,1},,{q})(q,0)=q,(q,1)=
2 (0+1)*(0+1)*
C Consider the setaccepted by thefinite automata,
M=({q},{0,1},,{q})(q,0)=,(q,1)=q
3 0*0*0*
D (Consider the setaccepted by the
finite automata,M=({q},{0,1},,{q})(q,0)=(q,1)=
4 1*1*1*
5 Set of all 0swhich are
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multiples ofthree andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q31.
A Consider the set acceptedby the finite automata,
M=({a,b,c},{0,1},,{q})(a,0)=a,(a.1)=b,(b,1)=b,
(b,0)=c,(c,0)=c,(c,1)=c
1
B Consider the set acceptedby the finite automata,
M=({q},{0,1},,{q})(q,0)=q,(q,1)=
2 0*0*1*1*
C Consider the set acceptedby the finite automata,
M=({q},{0,1},,{q})3 0*0*0*
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(q,0)=,(q,1)=qD (Consider the set accepted
by the finite automata,
M=({q},{0,1},,{q})(q,0)=(q,1)=
4 1*1*1*
5 Set of all0s whicharemultiplesof threeand four
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q32.
A Consider the set accepted bythe finite automata,
M=({q},{0,1},,{q})(q,0)=q,(q,1)=q
1 (01+10)*
B Consider the set accepted by 2 (0+1)*(0+1)*
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the finite automata,
M=({q},{0,1},,{q})(q,0)=q,(q,1)=
C Consider the set accepted bythe finite automata,
M=({q},{0,1},,{q})(q,0)=,(q,1)=q
3 0*0*0*
D Consider the set accepted bythe finite automata,
M=({q0,q1,q2,q3},{0,1},,{q})(q0,0)=q1,(q0,1)=q2,(q1,1)=q0,(q1,0)=q3,(q2,0)=q0,(q2,1)=q3,(q3,0)=q3,(q3,1)=q3
4 1*1*1*
5 Set of all 0swhich aremultiples of
three andfour
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
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Q33.A Consider the set accepted bythe finite automata,
M=({q},{0,1},,{q})(q,0)=q,(q,1)=q
1 Set of allstringsover {0,1}with anequalnumber of0s and 1s
whereeveryprefix hasat mostone more0 than 1 orat most
one more1 than a 0.
B Consider the set accepted bythe finite automata,
M=({q},{0,1},,{q})(q,0)=q,(q,1)=
2 The set ofall stringsover {0,1}
C Consider the set accepted by
the finite automata,M=({q},{0,1},,{q})
(q,0)=,(q,1)=q
3 The set of
all 0s
D Consider the set accepted bythe finite automata,
4 The set ofall 1s
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M=({q0,q1,q2,q3},{0,1},,{q})(q0,0)=q1,(q0,1)=q2,(q1,1)=q0,(q1,0)=q3,(q2,0)=q0,(q2,1)=q3,(q3,0)=q3,(q3,1)=q3
5 Set of all0s whicharemultiplesof three
and four6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q34.
A Consider the regular setdenoted by
(1+01+001)*(+0+00)1 Set of all
stringsover {0,1}with anequal
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number of0s and 1swhere
everyprefix hasat mostone more 0than 1 orat mostone more 1than a 0.
B Consider the set denoted by(0+1)*(00+11)
2 Theminimalfiniteautomatahas threestates
C Consider the set accepted by
the finite automata,M=({q},{0,1},,{q})
(q,0)=,(q,1)=q
3 The
minimalfiniteautomatahas 5states
D Consider the set accepted bythe finite automata,
M=({q0,q1,q2,q3},{0,1},,{q})(q0,0)=q1,(q0,1)=q2,(q1,1)=q0,(q1,0)=q3,(q2,0)=q0,(q2,1)=q3,(q3,0)=q3,(q3,1)=q3
4 The set ofall 1s
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5 Set of all0s whichare
multiplesof threeand four
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q35.
A Consider the regular setdenoted by
(1+01+001)*(+0+00)1 The
minimalfiniteautomatahas four
statesB Consider the set denoted by(0+1)*(00+11)
2 Theminimalfiniteautomatahas three
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states
C Consider the set denoted bythe regular expression
(00)*+(0000)*+(000000)*
3 Theminimal
finiteautomatahas 5states
D Consider the set accepted bythe finite automata,
M=({q0,q1,q2,q3},{0,1},,{q})(q0,0)=q1,(q0,1)=q2,(q1,1)=q0,(q1,0)=q3,(q2,0)=q0,(q2,1)=q3,(q3,0)=q3,(q3,1)=q3
4 Theminimalfiniteautomata
has twostates
5 Set of all0s whicharemultiples
of threeand four
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
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(iv) A->2,B->3,C->4,D->1
Q36.A Consider the regular setdenoted by(0+1)*1(0+1)(0+1)(0)
1 Theminimalfiniteautomatahas fourstates
B Consider the set denoted by(0+1)*(00+11)
2 Theminimalfiniteautomatahas 8states
C Consider the set denoted bythe regular expression
(00)*+(0000)*+(000000)*
3 Theminimal
finiteautomatahas 5states
D Consider the set accepted bythe finite automata,
M=({q0,q1,q2,q3},{0,1},,{q})(q0,0)=q1,(q0,1)=q2,(q1,1)=q0,(q1,0)=q3,(q2,0)=q0,(q2,1)=q3,(q3,0)=q3,(q3,1)=q3
4 Theminimalfinite
automatahas twostates
5 Set of all
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0s whicharemultiples
of threeand four
6 (000)*
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q37.A Consider the
regular setthe set of allstrings over{0,1} notcontaining 1
as asubstring
1 The minimalfiniteautomatahas 5 states
B Consider theregular setthe set of allstrings over
2 The minimalfiniteautomatahas 2 states
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{0,1} notcontaining11 as a
substringC Consider theregular setthe set of allstrings over{0,1} notcontaining111as a
substring
3 The minimalfiniteautomatahas 3 states
D Consider theregular setthe set of allstrings over{0,1} notcontaining
1111 as asubstring
4 The minimalfiniteautomatahas 4 states
5 Set of all 0swhich aremultiples ofthree andfour
6 (000)*
Answer:
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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q38.
A Consider theregular set theset of all
strings over{0,1} notcontaining101 as asubstring
1 The minimalfiniteautomata
has 3 states
B Consider theregular set the
set of allstrings over{0,1} startingwith a 1 thatinterpreted asthe binaryrepresentation
of an integerare congruentto 0 modulo 5
2 The minimalfinite
automatahas 4 states
C Consider theregular set theset of all
3 The minimalfiniteautomata
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strings over{0,1} wherethe 10th
symbol fromthe right endis a 1
has 7 states
D Consider theregular set theset of allstrings over{0,1} ending
in 00
4 The minimalfiniteautomatahas 1024states
5 Tsheminimalfiniteautomatahas 1000states
6 No minimalfiniteautomataexists
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
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(iv) A->2,B->3,C->4,D->1
Q39.A Consider theregular setthe set of allstrings over{0,1} wherethe 1s aredivisible by
10 and the0s aredivisible by11
1 The minimalfiniteautomatahas 5 states
B Consider theregular setthe set of all
strings over{0,1} wherethe 0ss aredivisible the3 and the 1sby 2
2 The minimalautomatahas 110
states
C Consider the
regular setthe set of allstrings over{0,1} wherethe 0s aredivisible by 6
3 The minimal
finiteautomatahas 6 states
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and the 1sdivisible by 8
D Consider the
regular setthe set of allstrings over{0,1} notcontaining1111 as asubstring
4 The minimal
finiteautomatahas 48 states
5 The minimal
finiteautomatahas 89 states
6 The minimalfiniteautomatahas 890
states
Answer:
(i) A
1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
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Q40.
A Consider adeterministic
finiteautomatawith inputalphabet{0,1} of10^1000states whichhas no final
state
1 The empty string isnot accepted
B Consider adeterministicfiniteautomatawith inputalphabet
{0,1} of10^1000states whereall the statesare finalstates
2 The emptyset isaccepted
C Consider a
deterministicfiniteautomataover thealphabet{0,1} of
3 (0+1)* is
accepted
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10^1000states wherethe start state
is the finalstate
D Consider adeterministicfiniteautomata of10^1000states over
the alphabet{0,1} wherethe start stateis not a finalstate
4 The emptystring isacepted
5 0 is accepted
6 1 is accepted
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q41.
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A Consider anondeterministicfinite automata
with inputalphabet {0,1} of10^1000 stateswhich has nofinal state
1 The empty string isnot accepted
B Consider anondeterministicfinite automata
with inputalphabet {0,1} of10^1000 stateswhere all thestates are finalstates
2 The emptyset isaccepted
C Consider a
nondeterministicfinite automataover thealphabet {0,1} of10^1000 stateswhere the startstate is the final
state
3 (0+1)* is
accepted
D Consider anondeterministicfinite automataof 10^1000states over the
4 The emptystring isacepted
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alphabet {0,1}where the startstate is not a
final state 5 0 is accepted
6 1 is accepted
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q42.A Deterministic
finite automata1 r.e. sets
B Deterministicpush downautomata
2 Regular sets
C Nondeterministic
linear boundedauotmata
3 Deterministic
context freelanguages
D Deterministicturing machines
4 Contextsensititvelanaugages
5 Context free
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languages
6 Recursivesets
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q43.
A Nondeterministic
finite automata
1 r.e. sets
B push downautomata
2 Regular sets
C Nondeterministiclinear boundedauotmata
3 context freelanguages
D Nondeterministic
turing machines
4 Context sensitive
lanaugages5 Deterministiccontext freelanguageslanguages
6 Recursive sets
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q44.
A Two waydeterministicfinite automata
1 r.e. sets
B Deterministicpush down
automata
2 Regular sets
C Nondeterministiclinear boundedauotmata
3 Deterministiccontext freelanguages
D Multitape turingmachines
4 Contextsensitivelanaugages
5 Context freelanguages
6 Recursivesets
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q46.
A Halting 100pushdown tapemachines
1 r.e. sets
B Deterministicpush down
automata
2 Recursivesets
C Nondeterministiclinear boundedauotmata
3 Deterministiccontext freelanguages
D 10000 countermachines
4 Contextsensitivelanaugages
5 Context freelanguages
6 Regular sets
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q47.
A Turing machinesthat have no ink
1 r.e. sets
B Deterministicpush down
automata
2 Regular sets
C Nondeterministiclinear boundedauotmata
3 Deterministiccontext freelanguages
D Deterministicturing machines
4 Contextsensitivelanaugages
5 Context freelanguages
6 Recursivesets
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sets
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q50.
A Multidimensional,multitape,multiheadedturing machines
with 1098 pushdown tapes but noink
1 r.e. sets
B Deterministicpush downautomata
2 Regular sets
C Nondeterministic
linear boundedauotmata
3 Deterministic
context freelanguages
D Deterministicturing machines
4 Contextsensitivelanaugages
5 Context free
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languages
6 Recursivesets
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q51.
A Deterministicfinite automata
1 Recursivesets
B Deterministicpush downautomata
2 Regular sets
C Nondeterministiclinear boundedauotmata
3 Deterministiccontext freelanguages
D Deterministic
halting turingmachines
4 Context
sensititvelanaugages
5 Context freelanguages
6 R.e. sets
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q52.
A Type 3grammars
1 r.e. sets
B LR(k)grammars
2 Regular sets
C Type 1
grammars
3 Deterministic
context freelanguages
D Type 0grammars
4 Contextsensititvelanaugages
5 Context freelanguages
6 Recursivesets
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q53.
A Deterministicfinite automata
1 Type 0languages
B Deterministicpush downautomata
2 Type 3languages
C Nondeterministiclinear boundedauotmata
3 Deterministiccontext freelanguages
D Deterministic
turing machines
4 Type 1
languages5 Type 2
languages
6 Recursivesets
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
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(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q54.
A Deterministicfiniteautomata
1 Proceduresthatare notnecessarilyalgorithms
B Deterministicpush downautomata
2 Regular sets
C Halting twopushdowntapemachines
3 Deterministiccontext freelanguages
D Deterministicturing
machines
4 Algorithms
5 Context freelanguages
6 Recursive sets
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
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(iv) A->2,B->3,C->4,D->1
Q55.A The set of allstrings over{0,1} withany numberof 0s andany numberof 1s
1 Recursive setthat is notcontextsensitive
B The set of allstrings over{0,1} with anequalnumber of0s and 1s
2 Regular setbut not a dcfl
C The set of all
strings over{0,1,2} withan equalnumber of0s, 1s and2s.
3 Deterministic
context freelanguage
D The set of
regularexpressionswhosecomplementis empty
4 Context
sensititvelanguagethat is notcontext free
5 r.e but not
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recursive
6 Finite set
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q56.
A The set of allstrings over{0,1} with
any numberof 0s andany numberof 1s
1 Recursive setthat is notcontext
sensitive
B The set of allpalidromesover {0,1}
2 Regular setbut not a dcfl
C The set of allstrings over{0,1,2} withan equalnumber of0s, 1s and
3 context freelanguage
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strings over{0,1} with anequal
number of0s and 1s
but not a dcfl
C The set of allstrings over{0,1,2}of theform wwwhere w is astring in
{0,1,2}+
3 Deterministiccontext freelanguage
D The set ofregularexpressionswhosecomplementis empty
4 Contextsensititvelanguagethat is notcontext free
5 r.e but notrecursive
6 Finite set
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
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Q58.
A The set of allstrings over{0,1} withany numberof 0s andany numberof 1s
1 Recursive set
B The set of allstrings over{0,1} not ofthe form ww,w in {0,1}+
2 Regular setbut not a dcfl
C The set of allstrings over{0,1,2} with
an equalnumber of0s, 1s and2s.
3 context freelanguage
D The set ofregularexpressions
whoseintersectionis empty
4 Contextsensititvelanguage
that is notcontext free
5 r.e but notrecursive
6 Finite set
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q59.
A The set of allstrings over{0,1} withany numberof 0s and
any numberof 1s
1 Recursive set
B The set of allstrings over{0,1} with anunequalnumber of
0s and 1s
2 Regular setbut not a dcfl
C The set of allstrings over{0,1,2} withan equalnumber of
3 context freelanguage
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0s, 1s and2s.
D The set of
regularexpressionswhosecomplementis empty
4 Context
sensititvelanguagethat is notcontext free
5 r.e but notrecursive
6 Finite set
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q61.
A The set of all
strings over{0,1} notcontainingthreeconsecutive0s and not
1 Recursive set
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containingthreeconsecutive
1s.B The set of allstrings over{0,1,2} withan unequalnumber of0s and 1sor an
unequalnumber of1s and 2s
2 Regular setbut not a dcfl
C The set of allstringsprimes inunary.
3 context freelanguage
D The set ofregularexpressionswhosecomplementis empty
4 Contextsensititvelanguagethat is notcontext free
5 r.e but not
recursive6 Finite set
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q62.
A The set of allpowers of 2in binary
1 Recursive set
B The set of allstringspalidromesover a finite
alphabet
2 Regular setbut not a dcfl
C The set of allstringsprimes inunary.
3 context freelanguage
D The set ofregular
expressionswhosecomplementis empty
4 Contextsensititve
languagethat is notcontext free
5 r.e but notrecursive
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6 Finite set
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q63.
A The set of allpowers of 2in binary
1 Recursive set
B The set of all
strings withan equalnumber of0s and 1sor with twiceas many 0sas 1s.
2 Regular set
but not a dcfl
C The set of allstrings thatare notprimes inbinary.
3 context freelanguage
The set of 4 ContextD
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complement is empty languagethat is notcontext free
5 r.e but notrecursive
6 Finite set
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q65.A The set of all powers of
20 in base 201 Recursive
set
B {0^m1^n0^(m+n)|m,n>1} 2 Regular setbut not adcfl
C {wwRw|w in {0,1}+} 3 context
freelanguage
D The set of regularexpressions whosecomplement is empty
4 Contextsensititvelanguagethat is not
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context free
5 r.e but notrecursive
6 Finite set
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q66.
A The set of all powers of
20 in base 20
1 Recursive
setB {0^m1^n0^(m+n)|m,n>1} 2 Regular set
but not adcfl
C {a^nb^n^2|n>1} 3 contextfreelanguage
D The set of regularexpressions whosecomplement is empty
4 Contextsensititvelanguagethat is notcontext free
5 r.e but not
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recursive
6 Finite set
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q67.
A The set of all powers of20 in base 20
1 Recursiveset
B {0^m1^n0^(m+n)|m,n>1} 2 Regular set
but not adcfl
C {a^Ib^j|gcd(I,j)=1} 3 contextfreelanguage
D The set of regularexpressions whose
complement is empty
4 Contextsensititve
languagethat is notcontext free
5 r.e but notrecursive
6 Finite set
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q68.
A The set of all powers of200 in base 200
1 Recursiveset
B {0^m1^n0^(m+n)|m,n>1} 2 Regular setbut not adcfl
C {a^Ib^jc^k|I not equal toj not equal to k}
3 contextfreelanguage
D The set of regularexpressions whosecomplement is empty
4 Contextsensititvelanguagethat is not
context free 5 r.e but notrecursive
6 Finite set
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q69.
A The set of all strings ovesr{0,1} not containing0000000001111111100000as a substring
1 Finite set
B {0^m1^n0^(m+n)|m,n>1} 2 Regular set
but not adcfl
C {a^Ib^jc^k|I not equal to jnot equal to k}
3 contextfreelanguage
D {0^n1^n| n
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set notnecessarilya context
sensitivelanguage
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q70.
A S-a|aS|b|bS 1 Finite setB SaSb|ab 2 Regular set
but not a dcfl
C {a^Ib^jc^k|Inot equal to jnot equal to
k}
3 context freelanguage
D {0^n1^n|n
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5 r.e but notrecursive
6 Recursive set
notnecessarily acontextsensitivelanguage
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q71.
A S-a|aS|b|bS 1 Finite setB SaSa|bSb|a|b 2 Regular set
but not a
dcflC {a^Ib^jc^k|Inot equal to jnot equal to k}
3 context freelanguage
D {0^n1^n|n
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lakh} languagethat is notcontext free
5 r.e but notrecursive
6 Recursive setnotnecessarily acontextsensitivelanguage
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q72.
A S-a|aS|b|bS 1 Finite setB S
aSa|bSb|a|b 2 Regular setbut not a
dcfl
C SaSBC|aBCCBBCaBab
3 context freelanguage
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bBbbbCbccCcc
D S
a|b|c|d 4 Contextsensititvelanguagethat is notcontext free
5 r.e but notrecursive
6 Recursive setnotnecessarily acontextsensitivelanguage
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
(iv) A->2,B->3,C->4,D->1
Q73.
A S-a|aS|b|bS 1 Finite setB SaSa|bSb|a|b 2 Regular set but not
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B SaSa|bSb|a|b 2 Regular set but nota dcfl
C SaSBC|aBCCB
BCaBabbBbbbCbccCcc
3 context free
language
D SCWaDWaaaWWDEWaEEaCECWWDFWaFWFwaCFW
4 The set{a^nb^nc^n|n>=1}
5 r.e but notrecursive
6 Recursive set notnecessarily acontext sensitivelanguage
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
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(iv) A->2,B->3,C->4,D->1
Q75.A S-a|aS|b|bS 1 Unrestrictedgrammar
B SaSa|bSb|a|b 2 Regulargrammar
C SaSBC|aBCCBBCaBabbBbbbCbccCcc
3 Context freegrammar
D SCWaDWaaaWWDEWaEEaCECWWDFWaFWFwaCFW
4 Contextsensitivegrammar
5 r.e but notrecursive
6 Recursive set
notnecessarily acontextsensitivelanguage
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q76.
A S-a|aS|b|bS 1 Type 0B SaSa|bSb|a|b 2 Type 3C SaSBC|aBC
CBBCaBabbBbbbCbccCcc
3 Type 2
D SCWaDWaaaWWDEWaEEaCE
CWWDFWaFWFwaCFW
4 Type 1
5 r.e but notrecursive
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6 Type 4
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q77.
A All C programs 1 Unrestrictedgrammar
B SaSa|bSb|a|b 2 ProceduresC SaSBC|aBC
CBBCaBabbBbbbCbccCcc
3 Context free
grammar
D SCWaDWaaaWWD
EWaEEaCECWWDFWaFWFwaCFW
4 Contextsensitive
grammar
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5 Not r.e.
6 Recursive setnot
necessarily acontextsensitivelanguage
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q78.
A Halting C andJava programs
1 Unrestrictedgrammar
B SaSa|bSb|a|b 2 AlgorithmsC SaSBC|aBC
CBBCaB
abbBbbbCbccCcc
3 Context freegrammar
D SCWaDWaaaW
4 Contextsensitive
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WDEWaEEaCECWWD
FWaFWFwaCFW
grammar
5 r.e but notrecursive
6 Recursive setnotnecessarily acontextsensitivelanguage
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q79.
A r.e. sets 1 Closed undercomplementbut notunder union
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orintersection
B Recursive
sets
2 Not closed
undercomplementbut closedunder unionandintersection
C Context freelanguages
3 Closed underunion,
intersectionandcomplement
D Deterministiccontext freelanguages
4 Closed underunion andintersectionbut not
undercomplement
5 Not closedunder unionbut closedunderintersection
6 Not closedunder unionorcomplement
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D Deterministiccontext freelanguages
4 Closed underunion andintersection
but notundercomplement
5 Not closedunder unionbut closedunderintersection
6 Not closedunder unionorcomplement
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q81.
A Finite sets 1 Closed undercomplementbut not
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under unionorintersection
B Recursivesets 2 Not closedundercomplementbut closedunder unionandintersection
C Context free
languages
3 Closed under
union,intersectionandcomplement
D Deterministiccontext freelanguages
4 Closed underunion andintersection
but notundercomplement
5 Not closedunder unionbut closedunder
intersection6 Not closedunder unionorcomplement
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q82.
A The cliqueproblem
1 Decidable
B The 2-CNFproblem
2 NP-complete
C The
equivalenceof context-freelanguages
3 Is in P
D Equivalenceof finiteautomata
4 Undecidable
5 Not closed
under unionbut closedunderintersection
6 Not closed
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under unionorcomplement
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q83.
A TheHamiltonian
circuitproblem
1 Decidable
B The 2-CNFproblem
2 NP-complete
C Theequivalenceof a context-
free to *where isthe inputvocabulary.
3 Is in P
D The 4 Undecidable
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membershipproblem ofcontext
sensitivelanguages
5 Not closedunder unionbut closedunderintersection
6 Not closed
under unionorcomplement
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q84.
A Theknapsackproblem
1 Decidable
B The 2-CNF 2 NP-complete
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problem
C Theequivalence
of twodeterministicturingmachines
3 Is in P
D Whether acontext freelanguage isfinite,
infinite orempty
4 Undecidable
5 Not closedunder unionbut closedunderintersection
6 Not closedunder unionorcomplement
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6
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(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q86
A All formallanguages
1 Decidable
B The class ofregular sets
2 Areuncountable
C Whether aturingmachine willhalt on blanktape
3 Countablyinfinite
D Whether aturingmachine willever leave an
input region
4 Undecidable
5 Not closedunder unionbut closedunderintersection
6 Not closed
under unionorcomplement
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q87.
A {w$w| w in (0+1)*} 1 Finite set
B {wwR|in (0+1)*} 2 Deterministiccontext freelanguage
C {wwwwwwwwR|w
in(0+1)+}
3 Context free
languagethat is notdeterministic
D The set of all stringsnot containing0000000000001111000over {0,1} of length
less than 10^100000
4 Contextsensitivelanguagethat is not
context free5 Not closedunder unionbut closedunderintersection
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6 Not closedunder unionor
complement
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q88
A {0^100n 1^1000n|n>=1} 1 Finite set
B {0^n1^n|n>=1^n1^2n|n>=1 2 Deterministiccontext freelanguage
C {wwwwwwwwR|w in(0+1)+} 3 Context freelanguagethat is notdeterministic
D The set of all strings notcontaining0000000000001111000 over{0,1} of length less than10^100000
4 Contextsensitivelanguagethat is notcontext free
5 Not closed
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under unionbut closedunder
intersection6 Not closedunder unionorcomplement
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q89
A {ww| w in (0+1)*} 1 Thecomplementis not afinite set but
the set isfinite
B {wwR|in (0+1)*} 2 Thecomplementis a cfl
C {w$w|n(0+1)+} 3 The
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complementis not a clf
D The set of all strings
not containing0000000000001111000over {0,1} of lengthless than 10^100000
4 The
complementis a dcfl
5 Recursivebut not a csl
6 r.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q90.
A Sa 1 The langugegenerated isambiguouswith aninfinitenumber ofderivations
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for a
B SaSAA
a
2 Thelanguage
generated isunambiguous
C SaSA|BAaBb
3 Thelanguagegenerated isambiguouswith twoderivations
for aD SSS|a| 4 The
languagegenerated isambiguouswith threedistinct
derivationsfor a
5 Thelanguagegenerated isinherentlyambigugous
6 Thelanguagegenerated isr.e but notrecursive
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q91.
A EE+E|E*E|(E)|i 1 The langugegenerated isambiguouswith aninfinite
number ofderivationsfor a
B SaSAAa
2 Thelanguagegenerated isambiguous
and is the setof all Cexpressionsover + and *
C SaSA|B
3 Thelanguage
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AaBb
generated isambiguouswith two
derivationsfor a
D SSS|a| 4 Thelanguagegenerated isambiguouswith threedistinct
derivationsfor a
5 Thelanguagegenerated isinherentlyambigugous
6 Thelanguagegenerated isr.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
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(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q92.
A EE+E|E*E|(E)|i 1 Thelanguagegenerated isambiguouswith aninfinite
number ofderivationsfor a
B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isambiguous
and is theset of all Cexpressionsover + and *
C SaSA|BAaB
b
3 Thelanguagegenerated is
ambiguousand is theset of allregularexpressionsover {a,b}
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D SSS|a| 4 Thelanguagegenerated is
ambiguouswith threedistinctderivationsfor a
5 Thelanguagegenerated is
inherentlyambigugous
6 Thelanguagegenerated isr.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q93.
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A EE+E|E*E|(E)|i 1 Thelanguagegenerated is
ambiguouswith aninfinitenumber ofderivationsfor a
B EE+E|E.E|(E)|a|b|| 2 Thelanguage
generated isambiguousand is the setof all Cexpressionsover + and *
C EE+T|TTT*F|FF(E)|i
3 The
languagegenerated isanunambiguousgrammar forarithmeticexpressions
D S
SS|a| 4 Thelanguagegenerated isambiguouswith threedistinct
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derivationsfor a
5 The
languagegenerated isinherentlyambigugous
6 Thelanguagegenerated isr.e but not
recursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q94.
A E
E+E|E*E|(E)|i 1 Thelanguagegenerated isall stringsover {a,b} notof the form
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languagegenerated isr.e but not
recursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q95.
A EE+E|E*E|(E)|i 1 Thelanguagegenerated isambiguousand is the setof all stringsover {a,b}with an equal
number ofas and bs.
B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isambiguous
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and is the setof all Cexpressions
over + and *C EE+T|TTT*F|FF(E)|i
3 Thelanguagegenerated isanunambiguousgrammar forarithmetic
expressionsD SaSbS|bSaS| 4 The
languagegenerated isambiguouswith threedistinct
derivationsfor a
5 Thelanguagegenerated isinherentlyambigugous
6 Thelanguagegenerated isr.e but notrecursive
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Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q96.
A EE+E|E*E|(E)|i 1 Thelanguagegenerated isambiguousand is the set
of all stringsover{a,b}with twice asmany as asbs.
B EE+E|E.E|(E)|a|b|| 2 Thelanguage
generated isambiguousand is the setof all Cexpressionsover + and *
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C EE+T|TTT*F|FF(E)|i
3 Thelanguagegenerated is
anunambiguousgrammar forarithmeticexpressions
D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated is
ambiguouswith threedistinctderivationsfor a
5 Thelanguage
generated isinherentlyambigugous
6 Thelanguagegenerated isr.e but not
recursive
Answer:
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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q97.
A AaAb|abA1a|a A1SA1|A1 S|
1 Thelanguagegenerated is
ambiguousand is the setof all stringsover{a,b}with twice asmany as asbs.
B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isthe set of allstrings over{a,b} with theas greater
than the bs.C EE+T|TTT*F|FF(E)|i
3 Thelanguagegenerated isanunambiguous
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languagegenerated isambiguous
with threedistinctderivationsfor a
5 Thelanguagegenerated isinherently
ambigugous6 The
languagegenerated isr.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q99.
A EE+E|E*E|(E)|i 1 The
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languagegenerated is{a^I b^J
c^K|I notequal to J orJ not equal toK}
B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isambiguous
and is the setof all Cexpressionsover + and *
C EE+T|TTT*F|FF(E)|i
3 Thelanguagegenerated is
anunambiguousgrammar forarithmeticexpressions
D SA1|B1|C1|A1 C1SA1 A|A1 A C1S
B C1| A1 B C1AaAb|abBaBb|abA1a| a A1B1b|b B1C1c|c C1
4 Thelanguage
generated isambiguouswith threedistinctderivationsfor a
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5 Thelanguagegenerated is
inherentlyambigugous
6 Thelanguagegenerated isr.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q100.
A SaSa|bSb|cSc|dSd 1 Thelanguage
generated isambiguousand is the setof all stringsover{a,b}with twice as
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many as asbs.
B EE+E|E.E|(E)|a|b|| 2 Thelanguagegenerated isthe set of allpalidromesover {a,b,c,d}
C EE+T|TTT*F|FF(E)|i
3 Thelanguagegenerated is
anunambiguousgrammar forarithmeticexpressions
D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguage
generated isambiguouswith threedistinctderivationsfor a
5 The
languagegenerated isinherentlyambigugous
6 Thelanguage
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generated isr.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q101.
A SaSa|bSb|cSc|dSd 1 Thelanguage
generated isambiguousand is theset of allstringsover{a,b}with twice
as many asas bs.
B {a^I b^J c^K|I=max(J,K)} 2 Thelanguagegenerated isthe set of all
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palidromesover{a,b,c,d}
C E
E+T|TTT*F|FF(E)|i
3 Thelanguagegenerated isa a csl andnot a cfl
D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated is
ambiguouswith threedistinctderivationsfor a
5 Thelanguage
generated isinherentlyambigugous
6 Thelanguagegenerated isr.e but not
recursive
Answer:
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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q102.
A SaSa|bSb|cSc|dSd 1 Thelanguage
generated isambiguousand is theset of allstringsover{a,b}with twice
as many asas bs.
B {a^I b^J c^K|I=min(J,K} 2 Thelanguagegenerated isthe set of allpalidromes
over{a,b,c,d}
C EE+T|TTT*F|FF(E)|i
3 Thelanguagegenerated isa csl which
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is not a cfl
D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguage
generated isambiguouswith threedistinctderivationsfor a
5 Thelanguage
generated isinherentlyambigugous
6 Thelanguagegenerated isr.e but not
recursive
Answer:
(i) A
1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
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Q103.
A SaSa|bSb|cSc|dSd 1 Thelanguagegenerated isambiguousand is theset of allstringsover{a,b}with twice
as many asas bs.
B {a^n B^n c^I|I not equal ton}
2 Thelanguagegenerated isthe set of allpalidromes
over{a,b,c,d}
C EE+T|TTT*F|FF(E)|i
3 Thelanguagegenerated isa csl whichis not a cfl
D S
aSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isambiguouswith threedistinct
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derivationsfor a
5 The
languagegenerated isinherentlyambigugous
6 Thelanguagegenerated isr.e but not
recursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q104.
A S
aSa|bSb|cSc|dSd 1 Thelanguagegenerated isambiguousand is theset of all
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stringsover{a,b}with twice
as many asas bs.
B {a^m B^n c^I|n lies betweenm and 2I}
2 Thelanguagegenerated isthe set of allpalidromesover
{a,b,c,d}C EE+T|T
TT*F|FF(E)|I
3 Thelanguagegenerated isa csl whichis not a cfl
D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isambiguouswith threedistinctderivationsfor a
5 Thelanguagegenerated isinherentlyambigugous
6 The
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languagegenerated isr.e but not
recursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q105.
A SaSa|bSb|cSc|dSd 1 Thelanguagegenerated isambiguousand is theset of allstrings
over{a,b}with twiceas many asas bs.
B {a^n B^n c^I|I not equal ton}
2 Thelanguage
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generated isthe set of allpalidromes
over{a,b,c,d}
C {a^I b^J c^K|K=I+J} 3 Thelanguagegenerated isa csl whichis not a cfl
D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isa dcfl whichis notregular
5 Thelanguage
generated isinherentlyambigugous
6 Thelanguagegenerated isr.e but not
recursive
Answer:
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(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5
(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q106.
A SaSa|bSb|cSc|dSd 1 Thelanguagegenerated is
ambiguousand is theset of allstringsover{a,b}with twiceas many as
as bs.B {a^n B^n c^I|I not equal to
n}2 The
languagegenerated isthe set of allpalidromesover
{a,b,c,d}C {a^I b^J c^K|K
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D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated is
a cfl whichis not a dcfl
5 Thelanguagegenerated isinherentlyambigugous
6 The
languagegenerated isr.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
Q106.
A {a^I b^J c^J d^2 e^3I} 1 Thelanguage
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generated isambiguousand is the
set of allstringsover{a,b}with twiceas many asas bs.
B {a^n B^n c^I|I not equal ton}
2 Thelanguage is
a cfl and ifwe take thefirst half ofthe stringswe ger alanguagewhich is not
a cflC EE+T|T
TT*F|FF(E)|i
3 Thelanguagegenerated isa csl whichis not a cfl
D SaSbSaS|aSaSbS|bSaSaS| 4 Thelanguagegenerated isambiguouswith threedistinctderivations
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for a
5 Thelanguage
generated isinherentlyambigugous
6 Thelanguagegenerated isr.e but notrecursive
Answer:
(i) A1,B->2,C->3,D->4(ii) A->2,B->3,C->4,D->5(iii) A->3,B-4,C->5,D->6(iv) A->2,B->3,C->4,D->1
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NOTE:-The answer for all the above questions is choice(IV)
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