| A free construction of Kleene algebras with tests (2008) | |||||||||||||||
Abstract | |||||||||||||||
| In this paper we define Kleene algebra with tests in a slightly more general way than Kozen’s definition. Then we give an explicit construction of the free Kleene algebra with tests generated by a pair of sets. Moreover we show that our free Kleene algebra with tests is isomorphic to Kozen and Smith’s Kleene algebra with tests if their construction available, that is, a generator of the Boolean algebra is finite. Finally, we show that an infinitely-generated free Kleene algebra with tests in the sense of Kozen can be obtained from our Free algebra. 1 | |||||||||||||||
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