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#### Most Complex Regular Ideal Languages

(Discrete Mathematics and Theoretical Computer Science, 2016-10-17)

A right ideal (left ideal, two-sided ideal) is a non-empty language $L$ over an alphabet $\Sigma$ such that $L=L\Sigma^*$ ($L=\Sigma^*L$, $L=\Sigma^*L\Sigma^*$). Let $k=3$ for right ideals, 4 for left ideals and 5 for ...

#### Complexity of Right-Ideal, Prefix-Closed, and Prefix-Free Regular Languages

(Institute of Informatics: University of Szeged, 2017)

A language L over an alphabet E is prefix-convex if, for any words x, y, z is an element of Sigma*, whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free ...

#### Quotient Complexity of Bifix-, Factor-, and Subword-Free Regular Language

(Institute of Informatics: University of Szeged, 2014)

A language $L$ is prefix-free if whenever words $u$ and $v$ are in $L$ and $u$ is a prefix of $v$, then $u=v$. Suffix-, factor-, and subword-free languages are defined similarly, where by ``subword" we mean ``subsequence", ...

#### Quotient Complexities of Atoms in Regular Ideal Languages

(Institute of Informatics: University of Szeged, 2015)

A (left) quotient of a language L by a word w is the language w(-1) L = {x vertical bar wx is an element of L}. The quotient complexity of a regular language L is the number of quotients of L; it is equal to the state ...

#### In Search Of Most Complex Regular Languages

(World Scientific Publishing, 2013-09-01)

Sequences (L-n vertical bar n >= k), called streams, of regular languages L-n are considered, where k is some small positive integer, n is the state complexity of L-n, and the languages in a stream differ only in the ...

#### Complexity Of Atoms Of Regular Languages

(World Scientific Publishing, 2013-11-01)

The quotient complexity of a regular language L, which is the same as its state complexity the number of left quotients of L. An atom of a non-empty regular language L with n quotients is a non-empty intersection of the n ...

#### Quotient Complexity Of Star-Free Languages

(World Scientific Publishing, 2012-09-01)

The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the ...

#### Most Complex Regular Right-Ideal Languages

(Springer, 2014)

A right ideal is a language L over an alphabet Sigma that satisfies the equation L = L Sigma*. We show that there exists a sequence (Rn vertical bar n >= 3) of regular right-ideal languages, where R-n has n left quotients ...