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#### 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 ...

#### 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 Ideal Languages

(Elsevier, 2013-01-28)

A language L over an alphabet Σ is a right (left) ideal if it satisfies L=LΣ∗ (L=Σ∗L). It is a two-sided ideal if L=Σ∗LΣ∗, and an all-sided ideal if L=Σ∗L, the shuffle of Σ∗ with L. Ideal languages are not only of interest ...

#### 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 ...

#### Syntactic Complexities of Six Classes of Star-Free Languages

(Otto-von-Guericke-Universit¨at Magdeburg, 2012)

The syntactic complexity of a regular language is the cardinality of its syntactic semi-group. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, ...

#### Syntactic Complexity of Suffix-Free Languages

(Elsevier, 2017-09-05)

We solve an open problem concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a suffix-free language with n left quotients (that is, with state complexity n) is at most (n−1)n−2+n−2 ...

#### Complexity of Suffix-Free Regular Languages

(Elsevier, 2017-11-01)

We study various complexity properties of suffix-free regular languages. A sequence (Lk,Lk+1,…) of regular languages in some class, where n is the quotient complexity of Ln, is most complex if its languages Ln meet the ...

#### Syntactic Complexity of Regular Ideals

(Springer, 2017-08-04)

The state complexity of a regular language is the number of states in a minimal deterministic finite automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic ...

#### 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 ...