### Abstract

In this paper we consider the problem of comparing two SMDPs with respect to their time-dependent behaviour. We propose a hemimetric between processes, which we call simulation distance, measuring the least acceleration factor by which a process needs to speed up its actions in order to behave at least as fast as another process. We show that this distance can be computed in time O(n2(f(l)+k)+mn7) , where n is the number of states, m the number of actions, k the number of atomic propositions, and f(l) the complexity of comparing the residence-time between states. The theoretical relevance and applicability of this distance is further argued by showing that (i) it is suitable for compositional reasoning with respect to CSP-like parallel composition and (ii) has a logical characterisation in terms of a simple Markovian logic.

Original language | English |
---|---|

Title of host publication | Quantitative Evaluation of Systems : 15th International Conference, QEST 2018, Beijing, China, September 4-7, 2018, Proceedings |

Editors | Anabelle McIver, Andras Horvath |

Number of pages | 17 |

Publisher | Springer |

Publication date | 4 Sep 2018 |

Pages | 339-355 |

ISBN (Print) | 978-3-319-99153-5 |

ISBN (Electronic) | 978-3-319-99154-2 |

DOIs | |

Publication status | Published - 4 Sep 2018 |

Event | Quantitative Evaluation of Systems 2018 - Beijing, China Duration: 4 Sep 2018 → 7 Sep 2018 http://www.qest.org/qest2018/ |

### Conference

Conference | Quantitative Evaluation of Systems 2018 |
---|---|

Country | China |

City | Beijing |

Period | 04/09/2018 → 07/09/2018 |

Internet address |

Series | Lecture Notes in Computer Science |
---|---|

Volume | 11024 |

ISSN | 0302-9743 |

### Fingerprint

### Cite this

*Quantitative Evaluation of Systems: 15th International Conference, QEST 2018, Beijing, China, September 4-7, 2018, Proceedings*(pp. 339-355). Springer. Lecture Notes in Computer Science, Vol.. 11024 https://doi.org/10.1007/978-3-319-99154-2_21

}

*Quantitative Evaluation of Systems: 15th International Conference, QEST 2018, Beijing, China, September 4-7, 2018, Proceedings.*Springer, Lecture Notes in Computer Science, vol. 11024, pp. 339-355, Beijing, China, 04/09/2018. https://doi.org/10.1007/978-3-319-99154-2_21

**A Hemimetric Extension of Simulation for Semi-Markov Decision Processes.** / Pedersen, Mathias Ruggaard; Bacci, Giorgio; Larsen, Kim Guldstrand; Mardare, Radu Iulian.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - A Hemimetric Extension of Simulation for Semi-Markov Decision Processes

AU - Pedersen, Mathias Ruggaard

AU - Bacci, Giorgio

AU - Larsen, Kim Guldstrand

AU - Mardare, Radu Iulian

PY - 2018/9/4

Y1 - 2018/9/4

N2 - Semi-Markov decision processes (SMDPs) are continuous-time Markov decision processes where the residence-time on states is governed by generic distributions on the positive real line.In this paper we consider the problem of comparing two SMDPs with respect to their time-dependent behaviour. We propose a hemimetric between processes, which we call simulation distance, measuring the least acceleration factor by which a process needs to speed up its actions in order to behave at least as fast as another process. We show that this distance can be computed in time O(n2(f(l)+k)+mn7) , where n is the number of states, m the number of actions, k the number of atomic propositions, and f(l) the complexity of comparing the residence-time between states. The theoretical relevance and applicability of this distance is further argued by showing that (i) it is suitable for compositional reasoning with respect to CSP-like parallel composition and (ii) has a logical characterisation in terms of a simple Markovian logic.

AB - Semi-Markov decision processes (SMDPs) are continuous-time Markov decision processes where the residence-time on states is governed by generic distributions on the positive real line.In this paper we consider the problem of comparing two SMDPs with respect to their time-dependent behaviour. We propose a hemimetric between processes, which we call simulation distance, measuring the least acceleration factor by which a process needs to speed up its actions in order to behave at least as fast as another process. We show that this distance can be computed in time O(n2(f(l)+k)+mn7) , where n is the number of states, m the number of actions, k the number of atomic propositions, and f(l) the complexity of comparing the residence-time between states. The theoretical relevance and applicability of this distance is further argued by showing that (i) it is suitable for compositional reasoning with respect to CSP-like parallel composition and (ii) has a logical characterisation in terms of a simple Markovian logic.

KW - semi-markov process

KW - markov decision process

KW - simulation

KW - hemimetric

UR - http://www.scopus.com/inward/record.url?scp=85053162810&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-99154-2_21

DO - 10.1007/978-3-319-99154-2_21

M3 - Article in proceeding

SN - 978-3-319-99153-5

T3 - Lecture Notes in Computer Science

SP - 339

EP - 355

BT - Quantitative Evaluation of Systems

A2 - McIver, Anabelle

A2 - Horvath, Andras

PB - Springer

ER -