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In an intersection between a regular language and a DCFL, we always tend to promote regular language to DCFL and say that the result will be intersection between DCFL and DCFL but since DCFLs are not closed under intersection we say the result will be a CFL. But I feel the answer to the original question should be DCFL because I never came across a language which is an intersection between a Regular language and a DCFL which is not DCFL

Can you write a language which is an intersection between a DCFL and a regular language but not a DCFL.
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I was having the exact same trouble yesterday :P But after a long discussion concluded that intersection of regular language with any other language(dcfl, cfl, rec, re) is dcfl,cfl,rec,re respectively.

Intersection of languages which are strictly dcfl( i.e. not regular and only dcfl) may or may not be dcfl. What I mean to say is strictly dcfl languages are not closed under intersection.

https://gateoverflow.in/232494/dcfl-vs-cfl#c232561

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Intersection of regular language with any other language is always closed.

Regula $\cap$ DCFL = DCFL

this applies on any other language.

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