Hegel's Reflexion Semigroup Homomorphism and Entire Prototypes Semigroup of Regular Languages Maxtotypes Regular Languages Substitution Maximal Rewriting of a Regular Language at a Regular Substitution Membership Problem
Issue Date:
22-Nov-2010
Publisher:
University Press "Paisii Hilendarski", Plovdiv
Abstract:
The following statements are proven: A correspondence of a
semigroup in another one is a homomorphism if and only if when the entire
prototype of the product of images contains (always) the product of their entire
prototypes. The Kleene closure of the maximal rewriting of a regular language
at a regular language substitution contains in the maximal rewriting of the
Kleene closure of the initial regular language at the same substitution. Let the
image of the maximal rewriting of a regular language at a regular language
substitution covers the entire given regular language. Then the image of any
word from the maximal rewriting of the Kleene closure of the initial regular
language covers by the image of a set of some words from the Kleene closure
of the maximal rewriting of this given regular language everything at the same
given regular language substitution. The purposefulness of the ¯rst statement
is substantiated philosophically and epistemologically connected with the spirit
of previous mathematical results of the author. A corollary of its is indicated
about the membership problem at a regular substitution.