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#### 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, ...

#### 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 ...

#### Theory Of Atomata

(Elsevier, 2014-06-19)

We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "atomaton", whose states are the "atoms" of the language, that is, non-empty intersections of complemented or ...

#### Quotient Complexity Of Closed Languages

(Springer, 2014-02-01)

A language L is prefix-closed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix-, factor-, and subword-closed languages in an analogous way, where by factor we mean contiguous subsequence, ...

#### 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 ...

#### Syntactic Complexity Of R- And J-Trivial Regular Languages

(World Scientific Publishing, 2014-11-01)

The syntactic complexity of a subclass of the class of regular languages is the maximal cardinality of syntactic semigroups of languages in that class, taken as a function of the state complexity n of these languages. We ...

#### 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 ...

#### On The Complexity Of The Evaluation Of Transient Extensions Of Boolean Functions

(World Scientific Publishing, 2012-01-01)

Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions ...