## Omega algebra, demonic refinement algebra and commands

- Weak omega algebra and demonic refinement algebra are two ways of describing systems with finite and infinite iteration. We show that these independently introduced kinds of algebras can actually be defined in terms of each other. By defining modal operators on the underlying weak semiring, that result directly gives a demonic refinement algebra of commands. This yields models in which extensionality does not hold. Since in predicate-transformer models extensionality always holds, this means that the axioms of demonic refinement algebra do not characterise predicate-transformer models uniquely. The omega and the demonic refinement algebra of commands both utilise the convergence operator that is analogous to the halting predicate of modal μ-calculus. We show that the convergence operator can be defined explicitly in terms of infinite iteration and domain if and only if domain coinduction for infinite iteration holds.

Author: | Peter HöfnerGND, Bernhard MöllerGND, Kim Solin |
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URN: | urn:nbn:de:bvb:384-opus4-359294 |

Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/35929 |

ISSN: | 0302-9743OPAC |

Parent Title (English): | Lecture Notes in Computer Science |

Publisher: | Springer |

Type: | Article |

Language: | English |

Year of first Publication: | 2006 |

Publishing Institution: | Universität Augsburg |

Release Date: | 2017/07/21 |

Volume: | 4136 |

First Page: | 222 |

Last Page: | 234 |

Note: | Relations and Kleene algebra in computer science: 9th International Conference on Relational Methods in Computer Science and 4th International Workshop on Applications of Kleene Algebra, RelMiCS/AKA 2006, Manchester, UK, August/September, 2006; proceedings |

DOI: | https://doi.org/10.1007/11828563_15 |

Institutes: | Fakultät für Angewandte Informatik |

Fakultät für Angewandte Informatik / Institut für Informatik | |

Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |

Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |

Licence (German): | Deutsches Urheberrecht |