Complete and Independent Sets of Axioms of Kleene Algebra

Abstract

In general, some equations can be reduced from others (that is, some equations are not independent from others) in a set of axioms of an algebra Then, it is an important problem to find a complete and independent set of axioms, where each axiom is independent of each other. In this paper the research works on axioms of Kleene algebra are surveyed. At first, we show a given axiom of Kleene algebra is independent or not from the others by using the method of indeterminate coefficients. Next, through these investigations we can clarify the properties of each axiom of Kleene algebra and 32 kinds of complete and independent sets of axioms are shown.