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- W2969193078 abstract "The problem of emph{regular separability} asks, given two languages $K$ and $L$, whether there exists a regular language $S$ with $Ksubseteq S$ and $Scap L=emptyset$. This problem has recently been studied for various classes of languages. All the results on regular separability obtained so far exhibited a noteworthy correspondence with the intersection emptiness problem: In eachcase, regular separability is decidable if and only if intersection emptiness is decidable. This raises the question whether under mild assumptions, regular separability can be reduced to intersection emptiness and vice-versa. We present counterexamples showing that none of the two problems can be reduced to the other. More specifically, we describe language classes $mathcal{C_1}$, $mathcal{D_1}$, $mathcal{C_2}$, $mathcal{D_2}$ such that (i)~intersection emptiness is decidable for $mathcal{C_1}$ and $mathcal{D_1}$, but regular separability is undecidable for $mathcal{C_1}$ and $mathcal{D_1}$ and (ii)~regular separability is decidable for $mathcal{C_2}$ and $mathcal{D_2}$, but intersection emptiness is undecidable for $mathcal{C_2}$ and $mathcal{D_2}$." @default.
- W2969193078 created "2019-08-22" @default.
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- W2969193078 date "2019-08-12" @default.
- W2969193078 modified "2023-09-27" @default.
- W2969193078 title "Regular Separability and Intersection Emptiness are Independent Problems" @default.
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