On the expressive power of Kleene algebra with domain

• Kleene algebras with domain are more expressive than Kleene algebras with tests.
• Kleene algebras with domain are expressive for propositional Hoare logic.
• Kleene algebras with tests are not expressive for this formalism.

It is shown that antidomain semirings are more expressive than test semirings and that Kleene algebras with domain are more expressive than Kleene algebras with tests. It is also shown that Kleene algebras with domain are expressive for propositional Hoare logic whereas Kleene algebras with tests are not.