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A logical characterization of various classes of regular languages

Summary: A logical characterization of various
classes of regular languages
Argimiro Arratia
Departamento de Matem´aticas,
Universidad Sim´on Bol´ivar
Apartado 89000, Caracas 1080-A,
E-mail: 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


Source: Arratia, Argimiro A. - Departamento de Matemática Aplicada, Universidad de Valladolid


Collections: Mathematics