Semigroups Of Languages Research Articles

ORDERED SEMIGROUPS, UPPER-TRIANGULAR REFLEXIVE RELATIONS AND SEMIGROUPS OF LANGUAGES

We study the connection between the classes of semigroups of positive languages, upper-triangular reflexive relations over posets and semigroups of order-preserving and extensive transformations of sets. From our constructions we derive some interesting consequences also for the finite case. For example, we prove that the class of finite semigroups of languages coincides with the class of semigroups of reflexive upper-triangular binary relations on finite sets.

ORDERED AND $\mathcal{J}$-TRIVIAL SEMIGROUPS AS DIVISORS OF SEMIGROUPS OF LANGUAGES

A semigroup of languages is a set of languages considered with (and closed under) the operation of catenation. In other words, semigroups of languages are subsemigroups of power-semigroups of free semigroups. We prove that a (finite) semigroup is positively ordered if and only if it is a homomorphic image, under an order-preserving homomorphism, of a (finite) semigroup of languages. Hence it follows that a finite semigroup is [Formula: see text]-trivial if and only if it is a homomorphic image of a finite semigroup of languages.

Identity problem for quasiregular algebras over commutative semigroups and commutative semigroups of languages

In papers of one of the authors there were introduced quasiregular algebras over semigroups and their important role was advanced in language-theory research (cf. [1] and its accompanying bibliography). In particular, it was proven that quasiregular algebras over free semigroups give an algebraic characteristic to the class of contextfree languages similar to that which is given by regular Kleene algebras to the class of finite-automaton languages. All this made the problem of investigating quasiregular algebras over some semigroups or other an interesting and important one. Of particular interest here, as should be expected, is the identity problem for these algebras.

Commutative closure of regular semigroups of languages

Commutative closure of regular semigroups of languages