Browsing Mathematics (Faculty of) by Subject "state complexity"
Now showing items 1-12 of 12
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Algebraic Approaches to State Complexity of Regular Operations
(University of Waterloo, 2019-10-15)The state complexity of operations on regular languages is an active area of research in theoretical computer science. Through connections with algebra, particularly the theory of semigroups and monoids, many problems ... -
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 ... -
Complexity of proper prefix-convex regular languages
(Elsevier, 2019-10-01)A language L over an alphabet Σ is prefix-convex if, for any words x,y,z ∈ Σ*, whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages, which were ... -
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 ... -
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 ... -
Monoids and the State Complexity of the Operation root(<i>L</i>)
(University of Waterloo, 2004)In this thesis, we cover the general topic of state complexity. In particular, we examine the bounds on the state complexity of some different representations of regular languages. As well, we consider the state ... -
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 ... -
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 ... -
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 ... -
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 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 Complexities of Nine Subclasses of Regular Languages
(University of Waterloo, 2012-07-31)The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in ...