## Characteristic Formulae for Fixed-Point Semantics: A General Framework (2010)

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Venue: | UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE |

Citations: | 3 - 1 self |

### BibTeX

@MISC{Aceto10characteristicformulae,

author = {Luca Aceto and et al.},

title = {Characteristic Formulae for Fixed-Point Semantics: A General Framework},

year = {2010}

}

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### Abstract

The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed points of suitable functions. Such constructions and their proofs of correctness have been developed independently, but have a common underlying structure. This study provides a general view of characteristic formulae that are expressed in terms of logics with a facility for the recursive definition of formulae. It is shown how several examples of characteristic-formula constructions from the literature can be recovered as instances of the proposed general framework, and how the framework can be used to yield novel constructions. The paper also offers general results pertaining to the definition of co-characteristic formulae and of characteristic formulae expressed in terms of infinitary modal logics.

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Citation Context ...ive Works License.2 Characteristic Formulae for Fixed-Point Semantics: A General Framework An alternative approach to the specification and verification of reactive systems is that of model checking =-=[7, 6, 32]-=-. In this approach, automata are still the formalism of choice for the description of the actual behaviour of a concurrent system. However, specifications of the expected behaviour of a system are now... |

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Citation Context ...behavioural relations over finite labelled transition systems, Kripke structures and timed automata that are defined in terms of fixed points of suitable functions. (See, for instance, the references =-=[2, 5, 8, 13, 21, 23, 28]-=-.) Such constructions and their proofs of correctness have been developed independently, but have a common underlying structure. It is therefore natural to ask oneself whether one can provide a genera... |

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Citation Context ...to model checking, and we can translate automata to logic. (An investigation of the model checking problems that can be reduced to implementation verification may, for instance, be found in the paper =-=[4]-=-.) Characteristic formulae provide a very elegant connection between automata and logic, and between implementation verification and model checking. But, can they be constructed for natural, and suita... |

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(Show Context)
Citation Context ...ar fragment of CCS—up to bisimilarity using HML? The answer is negative because each formula in that logic can only describe a finite fragment of the initial behaviour of a process—see, for instance, =-=[1]-=- for a textbook presentation. However, as shown in, e.g., [18, 34], adding a facility for the recursive definition of formulae to (variants of) HML yields a logic that is powerful enough to support th... |

1 |
Lykke Pedersen & Jan Poulsen (2000): Characteristic formulae for timed automata
- Aceto, Ingolfsdottir, et al.
(Show Context)
Citation Context ...behavioural relations over finite labelled transition systems, Kripke structures and timed automata that are defined in terms of fixed points of suitable functions. (See, for instance, the references =-=[2, 5, 8, 13, 21, 23, 28]-=-.) Such constructions and their proofs of correctness have been developed independently, but have a common underlying structure. It is therefore natural to ask oneself whether one can provide a genera... |

1 |
Orna Gruemberg & Doron Peled
- Clarke
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(Show Context)
Citation Context ...ive Works License.2 Characteristic Formulae for Fixed-Point Semantics: A General Framework An alternative approach to the specification and verification of reactive systems is that of model checking =-=[7, 6, 32]-=-. In this approach, automata are still the formalism of choice for the description of the actual behaviour of a concurrent system. However, specifications of the expected behaviour of a system are now... |