Axiomatization of finite algebras
J Burghardt - Annual conference on artificial intelligence, 2002 - Springer
J Burghardt
Annual conference on artificial intelligence, 2002•SpringerWe 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. We show a sufficient condition for the
existence of a class A of prototype algebras for a given theory Θ. Such a set allows us to
prove Θ⊨ φ simply by testing whether ϕ holds in A.
always a regular tree language, and compute a finite axiom set for A. We give a rational
reconstruction of Barzdins' liquid flow algorithm. We show a sufficient condition for the
existence of a class A of prototype algebras for a given theory Θ. Such a set allows us to
prove Θ⊨ φ simply by testing whether ϕ holds in A.
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 . We show a sufficient condition for the existence of a class A of prototype algebras for a given theory Θ. Such a set allows us to prove Θ⊨φ simply by testing whether ϕ holds in A.
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