### Abstract

Original language | English |
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Title of host publication | Foundations of Software Science and Computation Structures : 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings |

Editors | Andrew Pitts |

Number of pages | 15 |

Volume | 9034 |

Publisher | Springer |

Publication date | 2015 |

Pages | 185-199 |

ISBN (Print) | 978-3-662-46677-3 |

ISBN (Electronic) | 978-3-662-46678-0 |

DOIs | |

Publication status | Published - 2015 |

Event | 18th International Conference on Foundations of Software Science and Computation Structures - Queen Mary University, London, United Kingdom Duration: 11 Apr 2015 → 18 Apr 2015 Conference number: 18 |

### Conference

Conference | 18th International Conference on Foundations of Software Science and Computation Structures |
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Number | 18 |

Location | Queen Mary University |

Country | United Kingdom |

City | London |

Period | 11/04/2015 → 18/04/2015 |

Series | Lecture Notes in Computer Science |
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ISSN | 0302-9743 |

### Fingerprint

### Cite this

*Foundations of Software Science and Computation Structures: 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings*(Vol. 9034, pp. 185-199). Springer. Lecture Notes in Computer Science https://doi.org/10.1007/978-3-662-46678-0_12

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*Foundations of Software Science and Computation Structures: 18th International Conference, FOSSACS 2015, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2015, London, UK, April 11-18, 2015, Proceedings.*vol. 9034, Springer, Lecture Notes in Computer Science, pp. 185-199, 18th International Conference on Foundations of Software Science and Computation Structures, London, United Kingdom, 11/04/2015. https://doi.org/10.1007/978-3-662-46678-0_12

**On the Total Variation Distance of Semi-Markov Chains.** / Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand; Mardare, Radu Iulian.

Research output: Contribution to book/anthology/report/conference proceeding › Book chapter › Research › peer-review

TY - CHAP

T1 - On the Total Variation Distance of Semi-Markov Chains

AU - Bacci, Giorgio

AU - Bacci, Giovanni

AU - Larsen, Kim Guldstrand

AU - Mardare, Radu Iulian

PY - 2015

Y1 - 2015

N2 - Semi-Markov chains (SMCs) are continuous-time probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line. This paper shows the tight relation between the total variation distance on SMCs and their model checking problem over linear real-time specifications. Specifically, we prove that the total variation between two SMCs coincides with the maximal difference w.r.t. the likelihood of satisfying arbitrary MTL formulas or omega-languages recognized by timed automata. Computing this distance (i.e., solving its threshold problem) is NP-hard and its decidability is an open problem. Nevertheless, we propose an algorithm for approximating it with arbitrary precision.

AB - Semi-Markov chains (SMCs) are continuous-time probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line. This paper shows the tight relation between the total variation distance on SMCs and their model checking problem over linear real-time specifications. Specifically, we prove that the total variation between two SMCs coincides with the maximal difference w.r.t. the likelihood of satisfying arbitrary MTL formulas or omega-languages recognized by timed automata. Computing this distance (i.e., solving its threshold problem) is NP-hard and its decidability is an open problem. Nevertheless, we propose an algorithm for approximating it with arbitrary precision.

U2 - 10.1007/978-3-662-46678-0_12

DO - 10.1007/978-3-662-46678-0_12

M3 - Book chapter

SN - 978-3-662-46677-3

VL - 9034

T3 - Lecture Notes in Computer Science

SP - 185

EP - 199

BT - Foundations of Software Science and Computation Structures

A2 - Pitts, Andrew

PB - Springer

ER -