Bisimulation for communicating piecewise deterministic Markov processes (CPDP's)

S.N. Strubbe; Arjan van der Schaft

doi:10.1007/b106766

Bisimulation for communicating piecewise deterministic Markov processes (CPDP's)

S.N. Strubbe, Arjan van der Schaft

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

20 Citations (Scopus)

Abstract

CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise Deterministic Markov Processes). We define CPDPs and the composition of CPDPs, and prove that the class of CPDPs is closed under composition. Then we introduce a notion of bisimulation for PDPs and CPDPs and we prove that bisimilar PDPs as well as bisimilar CPDPs have equal stochastic behavior. Finally, as main result, we prove the congruence property that, for a composite CPDP, substituting components by different but bisimilar components results in a CPDP that is bisimilar to the original composite CPDP (and therefore has equal stochastic behavior). © Springer-Verlag Berlin Heidelberg 2005.

Original language	Undefined
Title of host publication	Hybrid Systems: Computation and Control
Editors	M. Morari, L. Thiele
Place of Publication	Berlin
Publisher	Springer
Pages	623-639
Number of pages	17
ISBN (Print)	978-3-540-25108-8
DOIs	https://doi.org/10.1007/b106766
Publication status	Published - 2005

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Verlag
Number	3414
Volume	3414
ISSN (Print)	0302-9743

Keywords

IR-69166
METIS-228028
EWI-16849

Access to Document

10.1007/b106766

http://eprints.eemcs.utwente.nl/secure2/16849/01/fulltext.pdf

Cite this

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Bisimulation for communicating piecewise deterministic Markov processes (CPDP's). / Strubbe, S.N.; van der Schaft, Arjan.
Hybrid Systems: Computation and Control. ed. / M. Morari; L. Thiele. Berlin: Springer, 2005. p. 623-639 10.1007/b106766 (Lecture Notes in Computer Science; Vol. 3414, No. 3414).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Bisimulation for communicating piecewise deterministic Markov processes (CPDP's)

AU - Strubbe, S.N.

AU - van der Schaft, Arjan

PY - 2005

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N2 - CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise Deterministic Markov Processes). We define CPDPs and the composition of CPDPs, and prove that the class of CPDPs is closed under composition. Then we introduce a notion of bisimulation for PDPs and CPDPs and we prove that bisimilar PDPs as well as bisimilar CPDPs have equal stochastic behavior. Finally, as main result, we prove the congruence property that, for a composite CPDP, substituting components by different but bisimilar components results in a CPDP that is bisimilar to the original composite CPDP (and therefore has equal stochastic behavior). © Springer-Verlag Berlin Heidelberg 2005.

AB - CPDPs (Communicating Piecewise Deterministic Markov Processes) can be used for compositional specification of systems from the class of stochastic hybrid processes formed by PDPs (Piecewise Deterministic Markov Processes). We define CPDPs and the composition of CPDPs, and prove that the class of CPDPs is closed under composition. Then we introduce a notion of bisimulation for PDPs and CPDPs and we prove that bisimilar PDPs as well as bisimilar CPDPs have equal stochastic behavior. Finally, as main result, we prove the congruence property that, for a composite CPDP, substituting components by different but bisimilar components results in a CPDP that is bisimilar to the original composite CPDP (and therefore has equal stochastic behavior). © Springer-Verlag Berlin Heidelberg 2005.

KW - IR-69166

KW - METIS-228028

KW - EWI-16849

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BT - Hybrid Systems: Computation and Control

A2 - Morari, M.

A2 - Thiele, L.

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