Q. The number of strings of length 4 that are generated by the regular expression (0+1+|2+3+)*, where | is an alternation character and {+, *} are quantification characters, is:

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Q. Which of the following is FALSE ?

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Q. The regular grammar for the language L = {a^nb^m | n + m is even} is given by

(A) S → S1 | S2
S1 → a S1 | A1
A1 → b A1 | λ
S2 → aaS2 | A2
A2 → b A2 | λ
(B) S → S1 | S2
S1 → a S1 | a A1
S2 → aa S2 | A2
A1 → bA1 | λ
A2 → bA2 | λ
(C) S → S1 | S2
S1 → aaa S1 | aA1
S2 → aaS2 | A2
A1 → bA1 | λ
A2 → bA2 | λ
(D) S → S1 | S2
S1 → aa S1 | A1
S2 → aaS2 | aA2
A1 → bbA1 | λ
A2 → bbA2 | b

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Q. Let Σ = {a, b} and language L = {aa, bb}. Then, the complement of L is

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Q. Consider the following identities for regular expressions :

(a) (r + s)* = (s + r)*
(b) (r*)* = r*
(c) (r* s*)* = (r + s)*

Which of the above identities are true ?

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Q. Given the following two languages:

L1 = {uww^Rn | u, v, w ϵ {a, b}+}
L2 = {uwwR^n | u, v, w ϵ {a, b}+, |u| ≥ |v|}

Which of the following is correct ?

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Q. Given a Turing Machine:

M = ({q0, q1}, {0, 1}, {0, 1, B}, δ, B, {q1})
Where δ is a transition function defined as
δ (q0, 0) = (q0, 0, R)
δ (q0, B) = (q1, B, R)

The language L(M) accepted by Turing machine is given as :

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Q. Consider the following linear programming problem:

Max. z = 0.50x2 – 0.10x1
Subject to the constraints
2x1 + 5x2 ≤ 80
x1 + x2 ≤ 20
and x1, x2 ≥ 0

The total maximum profit (z) for the above problem is:

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Q. The regular expression for the complement of the language L = {anbm|n≥4, m≤3} is:

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Q. Consider the following two languages:

L1 = {0i1j | gcd(i,j)=1}
L2 is any subset of 0*.

Which of the following is correct?

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Q. Let L be the language generated by regular expression 0*10* and accepted by the deterministic finite automata M. Consider the relation RM defined by M. As all states are reachable from the start state, RM has ................ equivalence classes.

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Q. Let L = {0^n1^n | n≥0} be a context free language.
Which of the following is correct?

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Q. Given a Turing Machine

M = ({q0,q1,q2,q3}, {a,b}, {a,b,B}, δ, B, {q3})

Where δ is a transition function defined as

δ(q0,a) = (q1,a,R)
δ(q1,b) = (q2,b,R)
δ(q2,a) = (q2,a,R)
δ(q2,b) = (q3,b,R)

The language L(M) accepted by the Turing Machine is given as:

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Q. Match the following :

List - I                                                             List - II
(a) {a^n b^n|n > 0} is a deterministic                  (i) but not recursive language
context free language        
(b) The complement of {a^n b^n a^n|n > 0}         (ii) but not context free language
is a context free language
(c) {a^n b^n a^n} is context sensitive language (iii) but can not be accepted by a deterministic pushdown automation
(d) L is a recursive language                         (iv) but not regular

Codes :
     (a)   (b)   (c)   (d)

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Q. The language of all non-null strings of a’s can be defined by a context free grammar as
follow :

S→a S|S a| a

The word a^3 can be generated by ................ different trees.

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Q. The context free grammar given by

S→XYX
X→aX|bX|λ
Y→bbb

generates the language which is defined by regular expression:

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Q. There are exactly ................ different finite automata with three states x, y and z over the alphabet {a, b} where x is always the start state.

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Q. Given the following two languages :

L1={a^n b a^n|n>0}
L2={a^n b a^n b^n+1|n>0}

Which of the following is correct?

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Q. Consider a language A defined over the alphabet ∑={0, 1} as A = {0^[n/2] 1^n: n >= 0} .
The expression [n/2] means the floor of n/2, or what you get by rounding n/2 down to the nearest integer.

Which of the following is not an example of a string in A ?

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Q. A grammar G is LL(1) if and only if the following conditions hold for two distinct productions A → α | β

I. First (α) ∩ First (β) ≠ {a} where a is some terminal symbol of the grammar.
II. First (α) ∩ First (β) ≠ λ
III. First (α) ∩ Follow(A) = φ if λ є First (β)

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