A Free Construction of Kleene Algebras with Tests

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.

• Type: Conference
• Year: 2004
• Where: MPC
• Authors: Hitoshi Furusawa
• Keywords: Free Kleene Algebra, Kleene Algebra, Mathematics, MPC 2004, Smith’s Kleene Algebra