We show that the commutative closure of a star-free language is either star-free or not regular anymore. Actually, this property is shown to hold exactly for the closure with respect to a partial commutation corresponding to a transitive dependence relation. Moreover, the question whether the closure of a star-free language remains star-free is decidable precisely for transitive partial commuta...

Let φ : X → Y be a generically finite morphism. The purpose of this paper is to show how the OY -algebra structure on φ∗OX controls algebro-geometric aspects of X like the ring generation of graded rings associated to X and the very ampleness of line bundles on X . As the main application of this we prove some new results for certain regular surfaces X of general type. Precisely, we find the de...

Let P(Σ∗) be the semiring of languages, and consider its subset P(Σ). In this paper we define the language recognized by a weighted automaton over P(Σ) and a one-letter alphabet. Similarly, we introduce the notion of language recognition by linear recurrence equations with coefficients in P(Σ). As we will see, these two definitions coincide. We prove that the languages recognized by linear recu...

Capabilities of detecting temporal relations between two events can benefit many applications. Most of existing temporal relation classifiers were trained in a supervised manner. Instead, we explore the observation that regular event pairs show a consistent temporal relation despite of their various contexts, and these rich contexts can be used to train a contextual temporal relation classifier...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

We use nonstandard topology and the g-topology to characterize normal, almost-normal, regular, almost-regular, semiregular spaces. The cluster [resp. 0-cluster] set relation is used to characterize regular, almostregular [resp. strongly-regular] spaces. The Whyburn [resp. Dickman] filter bases are characterized and it is shown that the cluster [resp. f-cluster] set relation restricted to the do...

in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

Regular model checking is a framework for verifying parameterized and infinite-state systems. Techniques for regular model checking such as quotienting require a well-specified transition relation where the invariant of the system is represented implicitly. To relax the restriction, we propose a technique, which we call refinement of transition relation, and reconstruct and extend regular model...

In this paper we generalize some classical factorizations of a fuzzy relation into a symmetric component (indifference) and an asymmetric and regular component (regular fuzzy strict preference). From the above notions, we establish two properties of any regular fuzzy strict preference of a max-∗-transitive fuzzy relation, which are then used to obtain new fuzzy versions of Gibbard’s oligarchy t...