Use Context-Free Pumping Lemma to prove that that following languages over the alphabet {'x', 'y', 'z'}...

Use Context-Free Pumping Lemma to prove that that following languages over the alphabet {'x', 'y', 'z'} are NOT context-free

(a) {x^jy^2jz^j : j > 0}

(b) { x^myⁿz^k : m, n, k ≥ 0 and k = min(m,n) }

Expert Solution

venereology answered 2 months ago

Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y...

Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y = 10 × x | x and y are binary integers with no leading 0s, and y is two times x}. (The alphabet for this languages is {0, 1, ×, =}.) For example, 1010 = 10 × 101 is in L2, but 1010 = 10 × 1 is not. (b)Let Σ2 = {[ 0 0 ] , [ 0 1 ] , [ 1...

(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?}...

(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?} (20 pt.) ? = {? ∈ {?, #}∗ | ? = ??#??# ... #?? ??? ? ≥ ?, ?? ∈ ?∗ ??? ????? ?, ??? ?? ≠?? ???????? ?≠?} Hint: choose a string ? ∈ ? that contains ? #’s.

Use the Pumping Lemma to show that the following languages are not regular. (a) {ai bj...

Use the Pumping Lemma to show that the following languages are not regular. (a) {ai bj | i > j} (b) {apaq | for all integers p and q where q is a prime number and p is not prime}.

Use the pumping lemma to show that the following languages are not regular. A a. A1={0^n...

Use the pumping lemma to show that the following languages are not regular. A a. A1={0^n 1^n 2^n | n≥0} b. A2 = {www | w ∈ {a,b}∗} A c. A3 ={a^2^n | n≥0} (Here, a^2^n means a string of 2^n a’s.) A ={a3n |n > 0 }

Use the pumping lemma to show that the following languages are not regular (c) (5 pts)...

Use the pumping lemma to show that the following languages are not regular (c) (5 pts) Let Σ = {0, 1, −, =} and SUB = {x = y − z | x, y, z are binary integers, and x is the result of the subtraction of z from y}. For example: 1 = 1 − 0, 10 = 11 − 01 are strings in SUB but not 1 = 1 − 1 or 11 = 11 − 10.

Show that L2 = {anb2nan : n ≥ 0} is not context-free using the pumping lemma.

Prove the following Closure Properties with respect to Context Free Languages. 1. Show that Context Free...

Prove the following Closure Properties with respect to Context Free Languages. 1. Show that Context Free Languages are Closed under union(∪), concatenation(·), kleene star(*). (Hint: If L1 and L2 are Context Free languages then write Context Free grammar equivalent to L1 ∪ L2, L1 · L2, L∗ 1 ) 2. Show that if L1 and L2 are Context Free Languages, then L1 ∩ L2 is not necessarily Context Free. (Hint: Use Proof by Counter Example)

1. Pumping Lemma: a. Is the following language a regular language? (Use pumping lemma in proof.)...

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Do not use Pumping Lemma for Regular Expression to prove the following. You may think of...

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Use two different ways to prove X Y + Z = (X + Z)(Y + Z)....

Use two different ways to prove X Y + Z = (X + Z)(Y + Z). a) Use pure algebraic way b) k-maps

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