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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Q. Given the following grammars :

G1: S → AB|aaB

A → aA | ∈

B → bB | ∈

G2: S → A | B

A → a A b | ab

B → a b B | ∈

Which of the following is correct?

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Q. Let L be any language. Define even (W)  as the  strings  obtained by extracting from W the letters in the even-numbered positions and even (L) = {even (W) | W ԑ L}. We define another language Chop (L) by removing the two leftmost symbols of every string in L given by Chop(L) = {W | v W ԑ L,with | v | = 2}.

If L is regular language then

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Q. Given the following two grammars :

G1 :     S → AB | aaB

A → a | Aa

B → b

G2: S→ aSbS|bSaS|λ

Which statement is correct ?

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Q. Match the following:

List-I                                                            List-II

a. Chomsky Normal form                       i.  S→ bSS|aS|c

b. Greibach Normal form                        ii.  S→ aSb|ab

c. S-grammar                                           iii. S→ AS|a

                                                                         A→ SA|b

d. |LL grammar                                        iv. S→ aBSB

                                                                         B→ b

Codes:
a       b       c       d

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Q. Given the following two languages :

L1 = {anbn |n≥1} ∪ {a}

L2= {w C wR|we {a,b}*}

Which statement is correct ?

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Q. The solution of the recurrence relation of T(n) = 3T ( floor (n/4) ) +  n is

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

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Q. Which of the following is FALSE ?

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Q. Consider the languages L1 = ϕ, and L2 = {1}. Which one of the following represents
L1* U L2* L1* ?

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Q. Given the following statements :
(A) A class of languages that is closed under union and complementation has to be closed under intersection.
(B) A class of languages that is closed under union and intersection has to be closed under complementation.
Which of the following options is correct?

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Q. Given the following two languages:

L1 = {a^nb^n|n≥0, n≠100}
L2 = {w ϵ {a,b,c}*| na(w) = nb(w) = nc(w)}

Which of the following options is correct?

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Q. Given the following two statements:

A. L = {w|na(w) = nb(w)} is deterministic context free language, but not linear.
B. L = {an bn} U {an b2n} is linear, but not deterministic context free language.

Which of the following options is correct?

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Q. Which of the following pairs have different expressive power?

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Q. Which of the following statements is false?

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Q. Let C be a binary linear code with minimum distance 2t + 1 then it can correct upto ............bits of error.

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Q. From the given data below:

a b b a a b b a a b

which one of the following is not a word in the dictionary created by LZ-coding (the initial words are a, b)?

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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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