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 b^j | i > j}

(b) {a^pa^q | for all integers p and q where q is a prime number and p is not prime}.

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venereology answered 6 months ago

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.

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...

Using the pumping lemma for regular languages, show that language is not regular. b) L3= {0n...

Using the pumping lemma for regular languages, show that language is not regular. b) L3= {0n 1m, m = n+2 } Language= {0,1}

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

1. Pumping Lemma: a. Is the following language a regular language? (Use pumping lemma in proof.) L = {0n 1n 2n | n ≥ 0} b. What is (i.e., define) the CFL pumping lemma?

(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.

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

Do not use Pumping Lemma for Regular Expression to prove the following. You may think of Closure Properties of Regular Languages 1. Fix an alphabet. For any string w with |w| ≥ 2, let middle(w) be the string obtained by removing the first and last symbols of w. That is, Given L, a regular language on Σ, prove that f1(L) is regular, where f1(L) = {w : middle(w) ∈ L}

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

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