We study additive distances and quasi-distances between words. We show that every additive distance is finite. We then prove that every additive quasi-distance is regularity-preserving, that is, the neighborhood of any radius of a regular language with respect to an additive quasi-distance is regular. Finally, similar results will be proven for context-free, computable and computably enumerable...

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

We investigate if every quasi-minimal group is abelian, and give a positive answer for a quasi-minimal pure group having a ∅-definable partial order with uncountable chains. We also relate two properties of a complete theory in a countable language: the existence of a quasi-minimal model and the existence of a strongly regular type. As a consequence we derive the equivalence of conjectures on c...

In this paper we have defined anti fuzzy interior ideal in semigroups. We characterize regular, intra-regular and left (right) quasi-regular semigroups by the properties of their anti fuzzy ideals, anti fuzzy bi-ideals, anti fuzzy generalized bi-ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals.

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and...

In this paper we present and analyze a quasi-Monte Carlo method for solving elliptic boundary value problems. Our method transforms the given partial differential equation into an integral equation by employing a well known local integral representation. The kernel in this integral equation representation can be used as a transition density function to define a Markov process used in estimating...

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...