History
Kleene algebras were not defined by Kleene; he introduced regular expressions and asked for a complete set of axioms, which would allow derivation of all equations among regular expressions. The problem was first studied by John Horton Conway under the name of regular algebras. The axioms of Kleene algebras solve this problem, as was first shown by Dexter Kozen.
Read more about this topic: Kleene Algebra
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