 
Summary: A logical characterization of various
classes of regular languages
Argimiro Arratia
Departamento de Matem´aticas,
Universidad Sim´on Bol´ivar
Apartado 89000, Caracas 1080A,
Venezuela
Email: arratia@ma.usb.ve
A class of languages is defined from the operations of union, intersec
tion, complement, concatenation and a new operation which, for two given
languages A and B, and a fixed language V , called the context, builds the
set of words whose number of possible factorizations as three factors, the
prefix in A, the suffix in B, and the middle in the context, is congruent
to an integer modulus. An appropriate family of generalized quantifiers is
defined that, when added to first order logic, captures exactly the aforesaid
class of languages with respect to finite linearly ordered structures. It is
shown, using model theoretical tools, that our languages so constructed are
regular and how particular cases of this construction corresponds to various
classes of regular languages. The main tool that we have developed is a
theorem that characterizes equivalence of formulas in our logics in terms of
