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?
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) 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.
Determine whether or not the following languages are regular. If
the language is regular then give an NFA or regular expression for
the language. Otherwise, use the pumping lemma for regular
languages or closure properties to prove the language is not
regular.
1) L = { 0 n1 k : k ≤ n ≤ 2k}
2) L = { 0 n1 k : n > 0, k > 0 } È { 1 k0 n : k > 0, n...