Q. Assume, L is regular language. Let statements S1 and S2 be defined as :

S1 : SQRT(L) = { x| for some y with |y| = |x|^2, xy ∈L}
S2 : LOG(L) = { x| for some y with |y| = 2^|x|, xy ∈ L}

Which of the following is true ?

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

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Q. Given the following productions of a grammar :

S→ aA| aBB;
A→aaA |λ ;
B→ bB| bbC;
C→ B

Which of the following is true ?

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Q. The language accepted by the nondeterministic pushdown automaton

M= ({q0, q1, q2}, {a, b}, {a, b, z}, δ, q0, z, {q2}) with transitions
δ (q0 a, z) = { (q1 a), (q2 λ)};
δ (q1, b, a) = { (q1, b)}
δ (q1, b, b) ={ (q1 b)}, δ (q1, a, b) = { (q2, λ)}

is

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Q. The language L = {a^n b^n a^m b^m | n ≥ 0, m ≥ 0} is

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Q. Assume statements S1 and S2 defined as :

S1 : L2-L1 is recursive enumerable where L1 and L2 are recursive and recursive enumerable respectively.
S2 : The set of all Turing machines is countable.

Which of the following is true ?

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Q. Non-deterministic pushdown automaton that accepts the language generated by the grammar:

S→aSS | ab is

(A) δ(q0, λ, z) = { (q1, z)};
δ(q0, a, S) = { (q1, SS)}, (q1, B) }
δ(q0, b, B) = { (q1, λ)},
δ(q1, λ, z) = { (qf, λ)}

(B) δ(q0, λ, z) = { (q1, Sz)};
δ(q0, a, S) = { (q1, SS)}, (q1, B) }
δ(q0, b, B) = { (q1, λ)},
δ(q1, λ, z) = { (qf, λ)}

(C) δ(q0, λ, z) = { (q1, Sz)};
δ(q0, a, S) = { (q1, S)}, (q1, B) }
δ(q0, b, λ) = { (q1, B)},
δ(q1, λ, z) = { (qf, λ)}

(D) δ(q0, λ, z) = { (q1, z)};
δ(q0, a, S) = { (q1, SS)}, (q1, B) }
δ(q0, b, λ) = { (q1, B)},
δ(q1, λ, z) = { (qf, λ)}

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Q. Given L1 = L(a*baa*) and L2 = L(ab*)
The regular expression corresponding to language L3 = L1/L2 (right quotient) is given by

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Q. Given the production rules of a grammar G1 as

S1→AB | aaB
A→a | Aa
B→b

and the production rules of a grammar G2 as

S2→aS2bS2 | bS2aS2 | λ

Which of the following is correct statement?

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Q. Given a grammar : S1→Sc, S→SA|A, A→aSb|ab, there is a rightmost derivation S1=>Sc =>SAC=>SaSbc. Thus, SaSbc is a right sentential form, and its handle is

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Q. The equivalent production rules corresponding to the production rules

S→Sα1|Sα2|β1|β2 is

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Q. Given a Non-deterministic Finite Automation (NFA) with states p and r as initial and final states respectively transition table as given below

The minimum number of states required in Deterministic Finite Automation (DFA) equivalent to NFA is

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Q. The grammar with production rules S → aSb |SS|λ generates language L given by:

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Q. A pushdown automation M = (Q, Σ, Γ, δ, q0, z, F) is set to be deterministic subject to which of the following condition(s), for every q ∈ Q, a ∈ Σ ∪ {λ} and b ∈ Γ
(s1) δ(q, a, b) contains at most one element
(s2) if δ(q, λ, b) is not empty then δ(q, c, b) must be empty for every c ∈ Σ

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Q. For every context free grammar (G) there exists an algorithm that passes any w ∈ L(G) in number of steps proportional to

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Q. Match the following:

a. Context sensitive language          i. Deterministic finite automation
b. Regular grammar                            ii. Recursive enumerable
c. Context free grammar                     iii. Recursive language
d. Unrestricted grammar                     iv. Pushdown automation

Codes:
      a   b    c   d

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Q. The statements s1 and s2 are given as:

s1: Context sensitive languages are closed under intersection, concatenation, substitution and inverse homomorphism.
s2: Context free languages are closed under complementation, substitution and homomorphism.

Which of the following is correct statement?

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Q. Consider the following statements :

I. Recursive languages are closed under complementation.
II. Recursively enumerable languages are closed under union.
III. Recursively enumerable languages are closed under complementation.

Which of the above statements are true ?

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Q. Given the following statements :

(i) The power of deterministic finite state machine and nondeterministic finite state machine are same.
(ii) The power of deterministic pushdown automaton and nondeterministic pushdown automaton are same.

Which of the above is the correct statement(s) ?

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Q. Which is not the correct statement(s) ?

(i) Every context sensitive language is recursive.
(ii) There is a recursive language that is not context sensitive.

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