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.
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?
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...
Are the following languages over {a, b} regular? If they are
then prove it. If they are not prove it with the Pumping Lemma
a) {ap | p is a prime number}
b) {xax | x Î{a,b}*} (start by listing some strings
in, not in, the language
Formal Languages
Give a regular expression for each of the following
languages:
L2a = {w ? {0,1}* | w corresponds to the binary encoding of
non-negative integers that are evenly divisible by 4
L2b = {w ? {a,b}* | w contains at least one 'a' and exactly two
b's}
L2c = {w ? {0, 1, 2}* | w starts with a 2, ends with a 1 and
contains an even number of 0's}.