Axiomatization of Finite Algebras
Logic in Computer Science
2014-03-31 v1 Formal Languages and Automata Theory
Abstract
We show that the set of all formulas in n variables valid in a finite class A of finite algebras is always a regular tree language, and compute a finite axiom set for A. We give a rational reconstruction of Barzdins' liquid flow algorithm (Barzdin+Barzdin, 1991). We show a sufficient condition for the existence of a class A of prototype algebras for a given theory T. Such a set allows us to prove T |= p simply by testing whether p holds in A.
Keywords
Cite
@article{arxiv.1403.7347,
title = {Axiomatization of Finite Algebras},
author = {Jochen Burghardt},
journal= {arXiv preprint arXiv:1403.7347},
year = {2014}
}
Comments
14 pages, 5 figures, author address given in header is meanwhile outdated