# A coalgebraic approach to Kleene algebra with tests

Chen, Hubie and Pucella, R.
(2004)
A coalgebraic approach to Kleene algebra with tests.
*CoRR*
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## Abstract

Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. Since the known automata-theoretic presentation of Kleene algebra with tests does not lend itself to a coalgebraic theory, we define a new interpretation of Kleene algebra with tests expressions and a corresponding automata-theoretic presentation. One outcome of the theory is a coinductive proof principle, that can be used to establish equivalence of our Kleene algebra with tests expressions.

## Metadata

Item Type: | Article |
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School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |

Depositing User: | Sarah Hall |

Date Deposited: | 09 Mar 2021 16:50 |

Last Modified: | 09 Aug 2023 12:50 |

URI: | https://eprints.bbk.ac.uk/id/eprint/43355 |

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