PP-2009-41:
Gheerbrant, Amélie
(2009)
*Complete Axiomatization of the Stutter-Invariant Fragment of the Linear-time mu-calculus.*
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## Abstract

The logic \mu(U) is the fixpoint extension of the "Until"-only

fragment of linear-time temporal logic. It also happens to be the

stutter- invariant fragment of linear-time \mu-calculus

\mu(\diamond). We provide complete axiomatizations of \mu(U) on the

class of finite words and on the class of \omega-words. We introduce

for this end another logic, which we call \mu(\diamond\Gamma), and

which is a variation of \mu(\diamond) where the Next time operator is

replaced by the family of its stutter-invariant counterparts. This

logic has exactly the same expressive power as \mu(U). Using already

known results for \mu(\diamond), we first prove completeness for

\mu(\diamond\Gamma), which finally allows us to obtain completeness

for \mu(U).

Item Type: | Report |
---|---|

Report Nr: | PP-2009-41 |

Series Name: | Prepublication (PP) Series |

Year: | 2009 |

Uncontrolled Keywords: | Specification languages; Linear-time temporal logic; Linear-time mu-calculus; Stutter-invariancy; Complete axiomatization |

Subjects: | Language |

Date Deposited: | 12 Oct 2016 14:37 |

Last Modified: | 12 Oct 2016 14:37 |

URI: | https://eprints.illc.uva.nl/id/eprint/371 |

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