Which of the following is a non regular language?

Which of the following is a non regular language?

a. L= {wxwy | x,y,w∈(a+b)+}

b. L= {xwyw | x,y,w∈(a+b)+}

c. L= {wxyw | x,y,w∈(a+b)+}

d. All of these

9Comments
Rohit Choudhary
9 Jan 2016 08:53 am

They all are looking regular to me.. :-/

lucky
9 Jan 2016 09:40 am

to me too :/

Parimal Andhalkar
9 Jan 2016 10:22 am

c. L= {wxyw | x,y,w∈(a+b)+}

not regular

Arul
9 Jan 2016 11:27 am

can you explain why?

lucky
9 Jan 2016 11:28 am

Yes, this is the answer..but how?? plz explain

Parimal Andhalkar
9 Jan 2016 03:04 pm

let w= 110  x = 010   y= 011

wxyw = 110 010 011 110   = 110 (0+1)+  110 = w(0+1)+ w

pattern not possible.

∴ not regular

Sayantan Banerjee
9 Jan 2016 03:41 pm

wxyw is not regular as the begining string and ending string have to be the same with xy in between , and hence w needs to be stored somewhere so that it can be compared with the ending string. So not regular .

Antonio Anastasio Bruto da
29 Oct 2017 07:22 pm

This is CORRECT. The language reduces to L = {wxw | x and w are any string over the alphabet} You can prove that the language is non-regular using the pumping lemma for regular languages.

meet @meet
9 Jan 2016 05:47 pm

What about option A and B?