### Abstract

Labelled weighted transition systems (LWSs) are transition systems labelled with actions and real numbers. The numbers represent the costs of the corresponding actions in terms of resources. Recursive Weighted Logic (RWL) is a multimodal logic that expresses qualitative and quantitative properties of LWSs. It is endowed with simultaneous recursive equations, which specify the weakest properties satisfied by the recursive variables. We demonstrate that RWL is sufficiently expressive to characterize weighted-bisimilarity of LWSs. In addition, we prove that the logic is decidable, i.e., the satisfiability problem for RWL can be algorithmically solved.

Original language | English |
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Title of host publication | Perspectives of System Informatics - 9th International Ershov Informatics Conference, PSI 2014, Revised Selected Papers |

Editors | Irina Virbitskaite, Andrei Voronkov, Irina Virbitskaite |

Publisher | Springer-Verlag |

Pages | 216-231 |

Number of pages | 16 |

ISBN (Print) | 9783662468227 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

Event | 9th International Ershov Informatics Conference on Perspectives of System Informatics, PSI 2014 - St. Petersburg, Russian Federation Duration: 24 Jun 2014 → 27 Jun 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8974 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 9th International Ershov Informatics Conference on Perspectives of System Informatics, PSI 2014 |
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Country | Russian Federation |

City | St. Petersburg |

Period | 24/06/14 → 27/06/14 |

### Fingerprint

### Keywords

- Hennessy-Milner property
- labelled weighted transition system
- maximal fixed point
- satisfiability

### Cite this

*Perspectives of System Informatics - 9th International Ershov Informatics Conference, PSI 2014, Revised Selected Papers*(pp. 216-231). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8974). Springer-Verlag. https://doi.org/10.1007/978-3-662-46823-4_18

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*Perspectives of System Informatics - 9th International Ershov Informatics Conference, PSI 2014, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8974, Springer-Verlag, pp. 216-231, 9th International Ershov Informatics Conference on Perspectives of System Informatics, PSI 2014, St. Petersburg, Russian Federation, 24/06/14. https://doi.org/10.1007/978-3-662-46823-4_18

**Decidability and expressiveness of recursive weighted logic.** / Larsen, Kim Guldstrand; Mardare, Radu; Xue, Bingtian.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Decidability and expressiveness of recursive weighted logic

AU - Larsen, Kim Guldstrand

AU - Mardare, Radu

AU - Xue, Bingtian

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Labelled weighted transition systems (LWSs) are transition systems labelled with actions and real numbers. The numbers represent the costs of the corresponding actions in terms of resources. Recursive Weighted Logic (RWL) is a multimodal logic that expresses qualitative and quantitative properties of LWSs. It is endowed with simultaneous recursive equations, which specify the weakest properties satisfied by the recursive variables. We demonstrate that RWL is sufficiently expressive to characterize weighted-bisimilarity of LWSs. In addition, we prove that the logic is decidable, i.e., the satisfiability problem for RWL can be algorithmically solved.

AB - Labelled weighted transition systems (LWSs) are transition systems labelled with actions and real numbers. The numbers represent the costs of the corresponding actions in terms of resources. Recursive Weighted Logic (RWL) is a multimodal logic that expresses qualitative and quantitative properties of LWSs. It is endowed with simultaneous recursive equations, which specify the weakest properties satisfied by the recursive variables. We demonstrate that RWL is sufficiently expressive to characterize weighted-bisimilarity of LWSs. In addition, we prove that the logic is decidable, i.e., the satisfiability problem for RWL can be algorithmically solved.

KW - Hennessy-Milner property

KW - labelled weighted transition system

KW - maximal fixed point

KW - satisfiability

UR - http://www.scopus.com/inward/record.url?scp=84942532191&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-46823-4_18

DO - 10.1007/978-3-662-46823-4_18

M3 - Conference contribution book

AN - SCOPUS:84942532191

SN - 9783662468227

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 216

EP - 231

BT - Perspectives of System Informatics - 9th International Ershov Informatics Conference, PSI 2014, Revised Selected Papers

A2 - Virbitskaite, Irina

A2 - Voronkov, Andrei

A2 - Virbitskaite, Irina

PB - Springer-Verlag

ER -