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- W2962772080 abstract "A right ideal (left ideal, two-sided ideal) is a non-empty language $L$ over an alphabet $Sigma$ such that $L=LSigma^*$ ($L=Sigma^*L$, $L=Sigma^*LSigma^*$). Let $k=3$ for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences ($L_n mid n ge k $) of right, left, and two-sided regular ideals, where $L_n$ has quotient complexity (state complexity) $n$, such that $L_n$ is most complex in its class under the following measures of complexity: the size of the syntactic semigroup, the quotient complexities of the left quotients of $L_n$, the number of atoms (intersections of complemented and uncomplemented left quotients), the quotient complexities of the atoms, and the quotient complexities of reversal, star, product (concatenation), and all binary boolean operations. In that sense, these ideals are most complex languages in their classes, or universal witnesses to the complexity of the various operations." @default.
- W2962772080 created "2019-07-30" @default.
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- W2962772080 date "2016-10-17" @default.
- W2962772080 modified "2023-10-18" @default.
- W2962772080 title "Most Complex Regular Ideal Languages" @default.
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- W2962772080 doi "https://doi.org/10.46298/dmtcs.1343" @default.
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