Normal Forms for Elements of the -Continuous Kleene Algebras
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Normal Forms for Elements of the ${}^*$-Continuous Kleene Algebras $K\mathop{\otimes_{\cal R}} C_2'$
Mark Hopkins, Hans Leiß
AbstractThe tensor product of the -continuous Kleene algebra with the polycyclic -continuous Kleene algebra over two bracket pairs contains a copy of the fixed-point closure of : the centralizer of in . We prove a representation of elements of by automata \`a la Kleene and refine it by normal form theorems that restrict the occurrences of brackets on paths through the automata. This is a foundation for a calculus of context-free expressions. We also show that validates a relativized form of the ``completeness property'' that distinguishes the bra-ket -continuous Kleene algebra from the polycyclic one.