Browsing Mathematics (Faculty of) by Author "Brzozowski, Janusz"
Now showing items 1-20 of 25
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Complexity Of Atoms Of Regular Languages
Brzozowski, Janusz; Tamm, Hellis (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 Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages
Brzozowski, Janusz; Sinnamon, Corwin (Springer, 2017-03-06)A language L over an alphabet Σ is suffix-convex if, for any words x,y,z∈Σ∗, whenever z and xyz are in L, then so is yz. Suffix-convex languages include three special cases: left-ideal, suffix-closed, and suffix-free ... -
Complexity of Proper Prefix-Convex Regular Languages
Brzozowski, Janusz; Sinnamon, Corwin (Springer, 2017-06-27)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 proper prefix-convex regular languages
Brzozowski, Janusz; Sinnamon, Corwin (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
Brzozowski, Janusz; Sinnamon, Corwin (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 ... -
Complexity of Suffix-Free Regular Languages
Brzozowski, Janusz; Szykuła, Marek (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 ... -
In Search Of Most Complex Regular Languages
Brzozowski, Janusz (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 ... -
Large Aperiodic Semigroups
Brzozowski, Janusz; Szykuła, Marek (World Scientific Publishing, 2015-11-01)We search for the largest syntactic semigroups of star-free languages having n left quotients; equivalently, we look for the largest transition semigroups of aperiodic finite automata with n states. We first introduce ... -
Most Complex Non-returning Regular Languages
Brzozowski, Janusz; Davies, Sylvie (Springer, 2017-07-03)A regular language L is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jirásková derived upper bounds on the state complexity of ... -
Most Complex Regular Ideal Languages
Liu, Bo Yang Victor; Davies, Sylvie; Brzozowski, Janusz (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
Brzozowski, Janusz; Davies, Gareth (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 ... -
On The Complexity Of The Evaluation Of Transient Extensions Of Boolean Functions
Brzozowski, Janusz; Li, Baiyu; Ye, Yuli (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 ... -
Quotient Complexities of Atoms in Regular Ideal Languages
Brzozowski, Janusz; Davies, Sylvie (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
Brzozowski, Janusz; Jirásková, Galina; Baiyu, Li; Smith, Joshua (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 Closed Languages
Brzozowski, Janusz; Jirásková, Galina; Zou, Chenglong (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 Ideal Languages
Brzozowski, Janusz; Jirásková, Galina; Li, Baiyu (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 ... -
Quotient Complexity Of Star-Free Languages
Brzozowski, Janusz; Liu, Bo (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 Six Classes of Star-Free Languages
Brzozowski, Janusz; Li, Baiyu; Liu, David (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 Complexities of Some Classes of Star-Free Languages
Brzozowski, Janusz; Li, Baiyu (Springer, 2012)The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, ... -
Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages
Brzozowski, Janusz; Li, Baiyu; Ye, Yuli (Elsevier, 2012-08-31)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 ...