### Abstract

This paper proposes an algorithm for exact computation of bisimilarity distances between discrete-time Markov chains introduced by Desharnais et. al. Our work is inspired by the theoretical results presented by Chen et. al. at FoSSaCS'12, proving that these distances can be computed in polynomial time using the ellipsoid method. Despite its theoretical importance, the ellipsoid method is known to be inefficient in practice. To overcome this problem, we propose an efficient on-the-fly algorithm which, unlike other existing solutions, computes exactly the distances between given states and avoids the exhaustive state space exploration. It is parametric in a given set of states for which we want to compute the distances. Our technique successively refines over-approximations of the target distances using a greedy strategy which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated Markov chains shows that our algorithm improves, on average, the efficiency of the corresponding iterative algorithms with orders of magnitude.

Original language | English |
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Title of host publication | Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2013. |

Editors | N. Pieterman, S.A. Smolka |

Place of Publication | Berlin |

Publisher | Springer-Verlag |

Pages | 1-15 |

Number of pages | 15 |

ISBN (Print) | 9783642367410 |

DOIs | |

Publication status | Published - 5 Mar 2013 |

Event | 19th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013 - Rome, Italy Duration: 16 Mar 2013 → 24 Mar 2013 |

### 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 | 7795 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 19th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013 |
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Country | Italy |

City | Rome |

Period | 16/03/13 → 24/03/13 |

### Fingerprint

### Keywords

- Markov chain
- discount factor
- transportation problem
- exact computation
- greedy strategy

### Cite this

*Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2013.*(pp. 1-15). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7795 LNCS). Berlin: Springer-Verlag. https://doi.org/10.1007/978-3-642-36742-7_1

}

*Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2013..*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7795 LNCS, Springer-Verlag, Berlin, pp. 1-15, 19th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, 16/03/13. https://doi.org/10.1007/978-3-642-36742-7_1

**On-the-fly exact computation of bisimilarity distances.** / Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim G.; Mardare, Radu.

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

TY - GEN

T1 - On-the-fly exact computation of bisimilarity distances

AU - Bacci, Giorgio

AU - Bacci, Giovanni

AU - Larsen, Kim G.

AU - Mardare, Radu

PY - 2013/3/5

Y1 - 2013/3/5

N2 - This paper proposes an algorithm for exact computation of bisimilarity distances between discrete-time Markov chains introduced by Desharnais et. al. Our work is inspired by the theoretical results presented by Chen et. al. at FoSSaCS'12, proving that these distances can be computed in polynomial time using the ellipsoid method. Despite its theoretical importance, the ellipsoid method is known to be inefficient in practice. To overcome this problem, we propose an efficient on-the-fly algorithm which, unlike other existing solutions, computes exactly the distances between given states and avoids the exhaustive state space exploration. It is parametric in a given set of states for which we want to compute the distances. Our technique successively refines over-approximations of the target distances using a greedy strategy which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated Markov chains shows that our algorithm improves, on average, the efficiency of the corresponding iterative algorithms with orders of magnitude.

AB - This paper proposes an algorithm for exact computation of bisimilarity distances between discrete-time Markov chains introduced by Desharnais et. al. Our work is inspired by the theoretical results presented by Chen et. al. at FoSSaCS'12, proving that these distances can be computed in polynomial time using the ellipsoid method. Despite its theoretical importance, the ellipsoid method is known to be inefficient in practice. To overcome this problem, we propose an efficient on-the-fly algorithm which, unlike other existing solutions, computes exactly the distances between given states and avoids the exhaustive state space exploration. It is parametric in a given set of states for which we want to compute the distances. Our technique successively refines over-approximations of the target distances using a greedy strategy which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated Markov chains shows that our algorithm improves, on average, the efficiency of the corresponding iterative algorithms with orders of magnitude.

KW - Markov chain

KW - discount factor

KW - transportation problem

KW - exact computation

KW - greedy strategy

UR - http://www.scopus.com/inward/record.url?scp=84874447331&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36742-7_1

DO - 10.1007/978-3-642-36742-7_1

M3 - Conference contribution book

SN - 9783642367410

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

SP - 1

EP - 15

BT - Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2013.

A2 - Pieterman, N.

A2 - Smolka, S.A.

PB - Springer-Verlag

CY - Berlin

ER -