2 votes 2 votes Suppose that L is Context free and R is Regular. $A$) $L – R$ is necessarily Context free $B$) $R – L$ is necessarily Context free Which of the above statement/s is/are true? Theory of Computation context-free-language theory-of-computation identify-class-language + – dd asked Jan 7, 2017 • retagged Jul 4, 2017 by Arjun dd 1.3k views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply dd commented Jan 7, 2017 reply Follow Share is it only $A$ ? 1 votes 1 votes Kapil commented Jan 7, 2017 reply Follow Share Yes, and 2nd one is false for CFL and even RE but not for others. 3 votes 3 votes vijaycs commented Jan 7, 2017 reply Follow Share ^yes. A) True B) False ( not necessarily), because CFL is not closed under complementation. R-L = R INTERSECTION L' 2 votes 2 votes srestha commented Jan 7, 2017 reply Follow Share if L is DCFL , then B) is also true. As DCFL closed under complement 1 votes 1 votes gatesjt commented Jan 7, 2017 reply Follow Share @kapil u meant R-L is not R.E when L is RE right ? and true when L is recursive right ? 0 votes 0 votes Devshree Dubey commented Jan 7, 2017 reply Follow Share If possible pease support ur answer with an example. It'll be helpful indeed. :) 0 votes 0 votes Please log in or register to add a comment.
3 votes 3 votes 1) It's closure property. CFL is closed under Regular difference (Even every language is closed under regular difference). 2) R-L is not any standard thing , we have to do calculations to know about this so we can't say anything. Rupendra Choudhary answered May 29, 2017 Rupendra Choudhary comment Share Follow See all 0 reply Please log in or register to add a comment.