# How to prove that the language is regular

#### zulfi100

Joined Jun 7, 2012
556
Hi,
I have the following language:
L={a^n b^l a^k : n+l+k >5 }

How can I prove that the language is regular?

Zulfi.

#### WBahn

Joined Mar 31, 2012
24,688
This is Homework Help, not Homework Done For You.

How may times do we have to say this to you?

You constantly want people to guide you from the very beginning of a problem. That's not going to help you in the long run. YOU need to at least START down a solution path, even if that path turns out to be a dead end.

The whole point of learning any of this is so that YOU can become a problem solver -- someone who solves other people's problems. Unless you expect the people that hire you to solve their problems to always guide you on how to start, you better start learning how to start on your own.

So, what are the basic tools that you have available to establish whether or not a language is regular?

#### zulfi100

Joined Jun 7, 2012
556
This is Homework Help, not Homework Done For You.

How may times do we have to say this to you?

You constantly want people to guide you from the very beginning of a problem. That's not going to help you in the long run. YOU need to at least START down a solution path, even if that path turns out to be a dead end.

The whole point of learning any of this is so that YOU can become a problem solver -- someone who solves other people's problems. Unless you expect the people that hire you to solve their problems to always guide you on how to start, you better start learning how to start on your own.

So, what are the basic tools that you have available to establish whether or not a language is regular?
Hi,
<How may times do we have to say this to you?>
I think this is the first time. As an example you can check my recent posts. For all I started with my solution, but sometimes you must realize the incapabilities of human.

Any way I read an article, based upon that I can tell you. After posting this problem, I got some solutions from internet also but they are contradictory.

n+l+K>5. Based upon this, I can say that powers are linear, so its a regular language. Now how can I prove that. One solution is construction but we cant keep the count of n,l,k so that its greater than 5. So what else we can do?

Zulfi.

#### WBahn

Joined Mar 31, 2012
24,688
And how many of your threads have started with nothing more than some solution that you found on the internet?

What do you mean by "powers are linear" and what does that have to do with it being a regular language or not?

Is L = aⁿ bⁿ

a regular language since the powers are linear?

How many possible ways are there to have n+l+k such that the sum is NOT greater than 5?

#### zulfi100

Joined Jun 7, 2012
556
And how many of your threads have started with nothing more than some solution that you found on the internet?

What do you mean by "powers are linear" and what does that have to do with it being a regular language or not?

Is L = aⁿ bⁿ

a regular language since the powers are linear?

Hi,
I got following from geeksforgeeks:
The pattern of strings form an A.P.(Arithmetic Progression) is regular(i.e it’s power is in
form of linear expression),
but the pattern with G.P.(Geometric Progression) is not regular(i.e its power is in form of
non-linear expression) and it comes under class of Context Sensitive Language.
How many possible ways are there to have n+l+k such that the sum is NOT greater than 5?
0 + 0 +0=>1 ways
1+0+0=>3
2+0+0=>3
3+0+0=>3
4+0+0=>3
5+0+0=>3
===
1+1+0 = >3
2+2+0 = >3
==
2+1 +1 = >3
3+1+1 = >3
3+1 +0=>

May be less than 50.

a^nb^n is not regular even though its powers are linear.

This is confusing. That's why I put this question on the forum.

But interesting I have varied answers for this.

Zulfi.

#### WBahn

Joined Mar 31, 2012
24,688
So if there are a finite number of ways that have to be considered, what does that mean as far as the ability to construct a DFA?

#### zulfi100

Joined Jun 7, 2012
556
So if there are a finite number of ways that have to be considered, what does that mean as far as the ability to construct a DFA?
Document says that:
Every finite set represents a regular language.

Ok.

I will check more on this. To find a infinite language declared as regular. Also one proof says its not regular. I would try to find that proof also.

Thanks a lot.

Zulfi.