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[[Category: Non-GATE Questions from Automata Theory]] | [[Category: Non-GATE Questions from Automata Theory]] | ||
Consider
$L_1 = \{a^nb^nc^md^m | m,n \ge 1\}$
$L_2 = \{a^nb^n | n \ge1\}$
$L_3 = \{(a+b)^*\}$
(1) Intersection of $L_1$ and $L_2$ is
(A) Regular (B) CFL but not regular (C) CSL but not CFL (D) None of these
(2) $L_1$ - $L_3$ is
(A) Regular (B) CFL but not regular (C) CSL but not CFL (D) None of these
(1) Regular.
GATECSEL₁ ∩ L₂
= {abcd,aabbcd,aaabbbccdd,.....} ∩ {ab, aabb, aaabbb,....}
= ϕ
(2) CFL
L₁ - L₃ = L₁, hence CFL
Proof,
L₁ - L₃ = {abcd,aabbcd,aaabbbccdd,.....} - { ∊,a,b,ab,aab,.....}
= {abcd,aabbcd,aaabbbccdd,.....}
= L₁
Consider
$L_1 = \{a^nb^nc^md^m | m,n \ge 1\}$
$L_2 = \{a^nb^n | n \ge1\}$
$L_3 = \{(a+b)^*\}$
(1) Intersection of $L_1$ and $L_2$ is
(A) Regular (B) CFL but not regular (C) CSL but not CFL (D) None of these
(2) $L_1$ - $L_3$ is
(A) Regular (B) CFL but not regular (C) CSL but not CFL (D) None of these
(1) Regular.
L₁ ∩ L₂
= {abcd,aabbcd,aaabbbccdd,.....} ∩ {ab, aabb, aaabbb,....}
= ϕ
(2) CFL
L₁ - L₃ = L₁, hence CFL
Proof,
L₁ - L₃ = {abcd,aabbcd,aaabbbccdd,.....} - { ∊,a,b,ab,aab,.....}
= {abcd,aabbcd,aaabbbccdd,.....}
= L₁