Q. Given the following statements.

S1: The grammars S → asb | bsa |ss I a and s→ asb | bsa| a are not equivalent.
S2: The grammars S→. ss| sss | asb | bsa| λ and S → ss |asb |bsa| λ are equivalent.

Which of the following is true?

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Q. Pumping -lemma for context-free languages states :
Let Lbe an infinite context free language. Then there exists some positive integer m such that any w ∈ L with Iwl ≥m can be decomposed as w = uv xy Z with Ivxyl_________ and Ivy I such that uvz, xyZ
Z ∈ L for all z = 0, 1,2, .......

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Q. The Greibach normal form grammar for the language L = {an bn+1 | n ≥ 0 } is

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Q. Given the following statements:

S1: Every context-sensitive language L is recursive.
S2: There exists a recursive language that is not context sensitive.

Which statement is correct?

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Q. Shift-Reduce parsers perform the following :

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Q. The following Context-Free Grammar (CFG) :

S → aB | bA

A → a | as | bAA

B → b | bs | aBB

will generate

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Q. Which of the following is true?

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Q. The pushdown automation M = ( {q0, q1, q2}',{a, b}, {0, 1}, δ, q0,0, {q0}) with

δ (q0, a, 0) = {(q1,10)}

δ (q1,a, 1) = {(q1,11)}

δ (q1,b, 1) = {(q2 , λ)}

δ(q2 , b, 1) = {(q2 , λ)}

δ (q2 , A, 0) = {(q0, λ)}

Accepts the language

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Q. Given two languages:

L1= {(ab)n,ak I n> k, k >=0}

L2 = {an bm l n ≠ m}

Using pumping lemma for regular language, it can be shown that

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Q. Regular expression for the complement of language L = {a^n b^m I n ≥ 4, m ≤ 3} is

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Q. We can show that the clique problem is NP-hard by proving that

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Q. Given the recursively enumerable language (LRE), the context sensitive language (LCS) the recursive language (LREC) the context free language (LCF) and deterministic context free language (LDCF) The relationship between these families is given by

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Q. Match the following:

       List- I                                                List -II
a. Context free grammar               i. Linear bounded automaton
b. Regular grammar                     ii. Pushdown automaton
c. Context sensitive grammar     iii. Turing machine
d. Unrestricted grammar             iv. Deterministic finite automaton

code:
a   b    c    d

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Q. According to pumping lemma for context free languages:
Let L be an infinite context free language, then there exists some positive integer m such that any w ∈ L with I w I ≥ m can be decomposed as w = u v x y z

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Q. The equivalent production rules corresponding to the production rules

S → Sα1 | Sα2 | β1 | β2 

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Q. If all the production rules have single non - terminal symbol on the left side, the grammar defined is :

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Q. Minimal deterministic finite automaton for the language L = {0n | n ≥ 0 , n ≠ 4} will have

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Q. The regular expression corresponding to the language L where L = { x ∈{0, 1}* | x ends with 1 and does not contain substring 00 } is :

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Q. A context free grammar for L = { w | n0 (w) > n1 (w)} is given by :

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Q. Given the following two statements :

S1: If L1 and L2 are recursively enumerable languages over Σ, then L1 ⋃ L2 and L1 ⌒ L2 are also recursively enumerable.

S2: The set of recursively enumerable languages is countable.

Which of the following is correct?

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