Question

Let Σ = {0, 1}. Give a regular expression that expresses the language {w | w contains exactly two 0s}.

Answer #1

Here I am providing the regular expresssion for the given question.

Given that the language {w | w contains exactly two 0s}

That means we can have any number of 1's and 0's should be exactly 2

some possible strings are,

00,1010,001,100,1100,1001 etc.

So, The Regular Expression is : 1*01*01*

by using this expression we can generate different strings which starts with 0,ends with 0,starts with 1,ends with 0etc. But most important thing is that it will always contain 2 0's which is required solution.

Let L1 be the language of the Regular Expression 1(1
+ 0)*.
Let L2 be the language of the Regular Expression 11*
0.
Let L3 be the language of the Regular Expression 1*
0.
Which of the following statements are true?
L2 L1
L2 L3
L1 L2
L3 L2

Let Σ = {0, 1}. Consider the language A = {ww | w ∈
0Σ*}. Give a string in the language A that has length at
least p.

Let Σ = {0, 1}. Consider the language A = {w | w has an odd
length}. Give a string in the language A that has length at least
p.

What is the regular expression for the language L={w| w starts
with 1 and has odd length}? The alphabet of the language is {0,
1};

Let Σ = {0,1}. Prove that the language { w | w contains the
substring 01001 } is regular by providing a finite automaton to
recognize the language. Include a state diagram, formal
description, and informal justification for the correctness of your
automaton.

Let Σ = {a}, and let L be the language
L={an :nisamultipleof3butnisNOTamultipleof5}.
Is L a regular language? HINT: Maybe instead of an explicit DFA
or regular expression, you can find another argument.

Give a regular expression for each of the following sets:
a) set of all string of 0s and 1s beginning with 0 and end with
1.
b) set of all string of 0s and 1s having an odd number of
0s.
d) set of all string of 0s and 1s containing at least one 0.
e) set of all string of a's and b's where each a is followed by
two b's.
f) set of all string of 0s and...

Prove that the following language is regular. L3 = {w | if w
contains any 0’s, then it contains at least three of them}

Using Pumping lemma to prove the below language is not
regular
Let Σ2 = {[ 0 0 ] , [ 0 1 ] , [ 1 0 ] , [ 1 1 ]} . Consider each
row to be a binary number and let L3 = w ∈ Σ ∗ 2 | the bottom row
of w is the square of the top row of w . For example, [ 0 1 ] [ 0 0
] [ 1 0...

Let L ⊆ Σ* be a regular language. Suppose a ∈ Σ and
define L\a = {x : ax ∈ L }. Show that L\a is regular.

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