Axiomatization of Finite Algebras
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2014
- DOI:
- 10.48550/arXiv.1403.7347
- arXiv:
- arXiv:1403.7347
- Bibcode:
- 2014arXiv1403.7347B
- Keywords:
-
- Computer Science - Logic in Computer Science;
- Computer Science - Formal Languages and Automata Theory;
- 68Q45;
- 68T15;
- F.4.1;
- F.4.3;
- I.2.3
- E-Print:
- 14 pages, 5 figures, author address given in header is meanwhile outdated