GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
64 views

 

Consider the following languages: 

 $L_{1}= \big\{0^{n+m} \ 1^{k+l}\ | \ m=l, m,n,k,l \geq 1 \big\} $

$ L_{2}= \big\{0^{n}  \big(1^ {2}\big)^{m}\ | \ m,n\geq 0 \big\} $

Which of the following is true?

  1. $L_{1}$ is regular but not $L_{2}$
  2. $L_{2}$ is regular but not $L_{1}$
  3. $L_{1}$ and $L_{2}$ are not-regular
  4. $L_{1}$ and $L_{2}$ are regular

Is L1 regular ?

asked ago in Theory of Computation by Boss (7.3k points) 4 28 83
edited ago by | 64 views

I think L1 reduces to {0n0m1m1k}, therefore Context Free. Is it ?

 

Update: Snce n,k>=1, therefore, n and k can cover up the m of 0 and 1 respectively, so L1 becomes {0n1k}, which is regular.

both are reg lang
both Are Regular, considering L1, the minimum length of string is 0011,

Now for each and every case you can put m = l = 1, and thus make it regular. Now with the help of n and k, scaling them as much as you can, independently.

And L2 = {0*(11)*} which is also regular.

1 Answer

+2 votes
Best answer

L2 is clearly regular as it can be written as : 0* (11)* in regular expression form..

Given L1 :  0n+m 1k+l  |  m = l and m,n,k,l >= 1

Now the key thing here is to satisfy m = l , we can adjust n and k accordingly , thereby the given language reduces to :

       L1 :  01y  |  x,y >= 2   which is regular.

Hence D) should be the correct answer.

answered ago by Veteran (88.5k points) 15 58 294
selected ago by

Related questions

0 votes
1 answer
2
asked in Theory of Computation by iarnav Loyal (4.6k points) 4 39 112 | 39 views
+1 vote
1 answer
3


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23396 Points

  2. Bikram

    17078 Points

  3. Habibkhan

    8158 Points

  4. srestha

    6286 Points

  5. Debashish Deka

    5438 Points

  6. jothee

    4978 Points

  7. Sachin Mittal 1

    4772 Points

  8. joshi_nitish

    4344 Points

  9. sushmita

    3964 Points

  10. Rishi yadav

    3804 Points


Recent Badges

Great Answer Manali Sikdar
Popular Question LavTheRawkstar
Great Question jothee
Notable Question Priyanka23
Great Question khushtak
Good Question Ishrat Jahan
Good Answer Arjun
Revival Arjun
Nice Question Kathleen
Nice Answer janakyMurthy
27,316 questions
35,169 answers
84,075 comments
33,262 users