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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?

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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.

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Prateek Raghuvanshi asked Nov 10, 2017
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$L_1 =\{a^n b^m c^n \mid m,n \geq 0\}$ and $L_2=\{ a^n b^n\mid n\geq 0\}$. If $L=L_2-L_1$ then $L$ isfinite languageregular languageDCFL not DCFL