(DCFL U Reg) '

Question

Hi Guys,

What will be ${\left ( DCFL \cup Regular \right )} '$ ?

Comments

DCFL is closed under complementation.

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bro but it is closed under intersection with reg language.

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^ every class of language is closed under "intersection with regular language".

Answer 1

(DCFL U Regular)'  = DCFL'  ⋂ Regular' = DCFL  ⋂ Regular = (DCFL -> CFL -> CSL)  ⋂ (Reg -> CFL -> CSL )  == CSL.

Answer 2

Answer is DCFL.

${\left ( DCFL \cup Regular \right )}' = {DCFL}' \cap {Regular}' = {DCFL } \cap { Regular } = DCFL$

Comments

A set is not the same as its element. You can say Delhi Union India is India, but Delhi Intersection Bangalore is not Delhi. Now applying to the question here, you must first clarify what you meant in the question -- a DCFL language or the set of all DCFL languages.

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@Arjun ji I think answer should be DCFL for general case.