A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
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We propose a quasi-equational sound axiomatization of regular tree languages, called monodic tree Kleene algebra. The algebra is weaker than Kleene algebra introduced by Kozen. We find a subclass of regular tree languages, for which monodic tree Kleene algebra is complete. While regular tree expressions may have two or more kinds of place holders, the subclass can be equipped with only one kind of them. Along the lines of the original proof by Kozen, we prove the completeness theorem based on determinization and minimization of tree automata represented by matrices on monodic tree Kleene algebra.