On the complexity of computing the profinite closure of a rational language

Rational Codes and Free Profinite Monoids

It is well known that clopen subgroups of finitely generated free profinite groups are again finitely generated free profinite groups. Clopen submonoids of free profinite monoids need not be finitely generated nor free. Margolis, Sapir and Weil proved that the closed submonoid generated by a finite code (which is in fact clopen) is a free profinite monoid generated by that code. In this note we...

Monoid Kernels and Profinite Topologies on the Free Abelian Group

To each pseudovariety of abelian groups residually containing the integers, there is naturally associated a proonite topology on any nite rank free abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can eeectively compute membership in the closure of a subgroup and more generally, in the closure of a rational subset of such a ...

Decidability and Tameness in the Theory of Finite Semigroups

TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

The effect of language complexity and group size on knowledge construction: Implications for online learning

This  study  investigated  the  effect  of  language  complexity  and  group  size  on  knowledge construction in two online debates. Knowledge construction was assessed using Gunawardena et al.’s Interaction Analysis Model (1997). Language complexity was determined by dividing the  number  of  unique  words  by  total  words.  It  refers  to  the  lexical  variation.  The  results showed  that...