2 votes 2 votes if L1 = { anbncn | n>= 0 } and L2 = { anbmck | k,n,m>=0} L1 is CSL and L2 is regular. Now L3 = L1.(L2)*. Is L3 is regualar or CSL? Theory of Computation theory-of-computation context-sensitive regular-language + – AnilGoudar asked May 10, 2017 retagged Jun 4, 2017 by Arjun AnilGoudar 3.1k views answer comment Share Follow See all 17 Comments See all 17 17 Comments reply srestha commented May 10, 2017 reply Follow Share how L2 could be regular? 0 votes 0 votes Purvi Agrawal commented May 10, 2017 reply Follow Share L2 should be dcfl ? 0 votes 0 votes srestha commented May 10, 2017 reply Follow Share @Purvi of course it is DCFL 0 votes 0 votes Purvi Agrawal commented May 10, 2017 reply Follow Share Then what should be the answer mam ? 0 votes 0 votes srestha commented May 10, 2017 reply Follow Share See this closure propertieshttp://gatecse.in/closure-property-of-language-families/ Now, L2 is DCFL. But DCFL not closed under kleen star. So, L2 may or may not be DCFL. Now, L1.(L2)* = it is a concatenation operation. And, CSL closed under concatenation . So, result will be CSL 1 votes 1 votes AnilGoudar commented May 10, 2017 reply Follow Share Edited the question.. Sorry for my mistake 0 votes 0 votes Purvi Agrawal commented May 10, 2017 reply Follow Share Mam if dcfl does not satisfy closure property then we will look for cfl or csl and how do we decide ? I thought we see the language just of the higher type..why are we not considering cfl ? 0 votes 0 votes srestha commented May 11, 2017 reply Follow Share yes.. 0 votes 0 votes Akriti sood commented May 11, 2017 reply Follow Share @srestha,after concatenation,does'nt the language become regular?? 0 votes 0 votes Akriti sood commented May 11, 2017 reply Follow Share sorry..my mistake..:-)it will not be regular 0 votes 0 votes srestha commented May 11, 2017 reply Follow Share Akriti, question edited here :) 0 votes 0 votes Akriti sood commented May 11, 2017 reply Follow Share tell me one thing,if it was not a keen closure then would L3 be regular? i mean like this L3 =L1XL2 CROSS PEODUCT instead of concatenation 0 votes 0 votes AnilGoudar commented May 11, 2017 reply Follow Share It's I think L3 is regular 0 votes 0 votes srestha commented May 11, 2017 reply Follow Share @Akriti how do u find cross product in TOC? It is only in DBMS. symbols are different in each subject :) 0 votes 0 votes Purvi Agrawal commented May 11, 2017 reply Follow Share Yes there exists concatenation but no cross product in toc 0 votes 0 votes Akriti sood commented May 11, 2017 reply Follow Share so sorry,i mixed them..:-P 0 votes 0 votes arun yadav commented Oct 4, 2020 reply Follow Share Is L2 is regular? 0 votes 0 votes Please log in or register to add a comment.
8 votes 8 votes Regular L1 = { $\epsilon$, abc, aabbcc, ... } L2 = a*b*c* L3 is L1.(L2)*, means $a^nb^nc^n(a^*b^*c^*)^*$ The important thing to notice is that n can be 0. So L3 will be $(a^*b^*c^*)^*$. Which is regular. Dhruv Patel answered May 11, 2017 Dhruv Patel comment Share Follow See all 8 Comments See all 8 8 Comments reply Show 5 previous comments Dhruv Patel commented May 11, 2017 reply Follow Share @Archies09 Oh I see it now. Sorry. They are same :) 0 votes 0 votes Harsh181996 commented May 15, 2017 reply Follow Share So , shouldn't the answer be both ? Every Regular Language is a CSL right. 1 votes 1 votes Dhruv Patel commented May 15, 2017 reply Follow Share @Harsh That's correct. Every regular language is CSL. So both are correct. Though regular language answer is more specific. 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes R1(R2)* is simply (a+b+c)*....and hence regular joshi_nitish answered May 15, 2017 joshi_nitish comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes L1 is CSL and L2 is regular. then (L2)* will be reguler (by using closure properties) and now L1.(L2)*=CSL.Reguler(push up) CSL.CSL=CSL pawan kumarln answered May 11, 2017 pawan kumarln comment Share Follow See 1 comment See all 1 1 comment reply Gatecoder commented May 12, 2017 reply Follow Share correct i have also same explanation.. 0 votes 0 votes Please log in or register to add a comment.