Continuity Properties of Distances for Markov Processes

Manfred Jaeger; Hua Mao; Kim Guldstrand Larsen; Radu Iulian Mardare

doi:10.1007/978-3-319-10696-0_24

Continuity Properties of Distances for Markov Processes

Manfred Jaeger, Hua Mao, Kim Guldstrand Larsen, Radu Iulian Mardare

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

5 Citations (Scopus)

Abstract

In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable continuity properties for such distances are identified. We then establish a number of results that show that these two properties are in conflict, and not simultaneously fulfilled by any of our candidate natural distance functions. An impossibility result is derived that explains to some extent the fundamental difficulty we encounter.

Original language	English
Title of host publication	Quantitative Evaluation of Systems : 11th International Conference, QEST 2014, Florence, Italy, September 8-10, 2014. Proceedings
Editors	Gethin Norman, William Sanders
Volume	8657
Publisher	Springer
Publication date	2014
Pages	297-312
ISBN (Print)	978-3-319-10695-3
ISBN (Electronic)	978-3-319-10696-0
DOIs	https://doi.org/10.1007/978-3-319-10696-0_24
Publication status	Published - 2014
Event	11th International Conference on Quantitative Evaluation of SysTems (QEST 2014) - Auditorium al Duomo, Florence, Italy Duration: 8 Sept 2014 → 10 Sept 2014 Conference number: 11th

Conference

Conference	11th International Conference on Quantitative Evaluation of SysTems (QEST 2014)
Number	11th
Location	Auditorium al Duomo
Country/Territory	Italy
City	Florence
Period	08/09/2014 → 10/09/2014

Series	Lecture Notes in Computer Science
ISSN	0302-9743

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10.1007/978-3-319-10696-0_24

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title = "Continuity Properties of Distances for Markov Processes",

abstract = "In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable continuity properties for such distances are identified. We then establish a number of results that show that these two properties are in conflict, and not simultaneously fulfilled by any of our candidate natural distance functions. An impossibility result is derived that explains to some extent the fundamental difficulty we encounter.",

author = "Manfred Jaeger and Hua Mao and Larsen, {Kim Guldstrand} and Mardare, {Radu Iulian}",

year = "2014",

doi = "10.1007/978-3-319-10696-0_24",

language = "English",

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volume = "8657",

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publisher = "Springer",

pages = "297--312",

editor = "Gethin Norman and William Sanders",

booktitle = "Quantitative Evaluation of Systems",

address = "Germany",

note = "11th International Conference on Quantitative Evaluation of SysTems (QEST 2014) , QEST2014 ; Conference date: 08-09-2014 Through 10-09-2014",

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Jaeger, M, Mao, H, Larsen, KG & Mardare, RI 2014, Continuity Properties of Distances for Markov Processes. in G Norman & W Sanders (eds), Quantitative Evaluation of Systems: 11th International Conference, QEST 2014, Florence, Italy, September 8-10, 2014. Proceedings. vol. 8657, Springer, Lecture Notes in Computer Science, pp. 297-312, 11th International Conference on Quantitative Evaluation of SysTems (QEST 2014) , Florence, Italy, 08/09/2014. https://doi.org/10.1007/978-3-319-10696-0_24

Continuity Properties of Distances for Markov Processes. / Jaeger, Manfred; Mao, Hua; Larsen, Kim Guldstrand et al.
Quantitative Evaluation of Systems: 11th International Conference, QEST 2014, Florence, Italy, September 8-10, 2014. Proceedings. ed. / Gethin Norman; William Sanders. Vol. 8657 Springer, 2014. p. 297-312 (Lecture Notes in Computer Science).

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

TY - GEN

T1 - Continuity Properties of Distances for Markov Processes

AU - Jaeger, Manfred

AU - Mao, Hua

AU - Larsen, Kim Guldstrand

AU - Mardare, Radu Iulian

N1 - Conference code: 11th

PY - 2014

Y1 - 2014

N2 - In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable continuity properties for such distances are identified. We then establish a number of results that show that these two properties are in conflict, and not simultaneously fulfilled by any of our candidate natural distance functions. An impossibility result is derived that explains to some extent the fundamental difficulty we encounter.

AB - In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable continuity properties for such distances are identified. We then establish a number of results that show that these two properties are in conflict, and not simultaneously fulfilled by any of our candidate natural distance functions. An impossibility result is derived that explains to some extent the fundamental difficulty we encounter.

U2 - 10.1007/978-3-319-10696-0_24

DO - 10.1007/978-3-319-10696-0_24

M3 - Article in proceeding

SN - 978-3-319-10695-3

VL - 8657

T3 - Lecture Notes in Computer Science

SP - 297

EP - 312

BT - Quantitative Evaluation of Systems

A2 - Norman, Gethin

A2 - Sanders, William

PB - Springer

T2 - 11th International Conference on Quantitative Evaluation of SysTems (QEST 2014)

Y2 - 8 September 2014 through 10 September 2014

ER -

Jaeger M, Mao H, Larsen KG, Mardare RI. Continuity Properties of Distances for Markov Processes. In Norman G, Sanders W, editors, Quantitative Evaluation of Systems: 11th International Conference, QEST 2014, Florence, Italy, September 8-10, 2014. Proceedings. Vol. 8657. Springer. 2014. p. 297-312. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-10696-0_24

Continuity Properties of Distances for Markov Processes

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