## Abstract

We take a dual view of Markov processes – advocated by Kozen – as transformers of bounded measurable functions. We redevelop the theory of labelled Markov processes from this view point, in particular we explore approximation theory. We obtain three main results:

(i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximation. (iii) It is possible to show that there is a minimal bisimulation equivalent to a process obtained as the limit of the finite approximants.

(i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximation. (iii) It is possible to show that there is a minimal bisimulation equivalent to a process obtained as the limit of the finite approximants.

Original language | English |
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Title of host publication | Automata, Languages and Programming |

Subtitle of host publication | 36th Internatilonal Collogquium, ICALP 2009, Rhodes, greece, July 5-12, 2009, Proceedings, Part II |

Editors | Susanne Albers, Alberto Marchetti-Spaccamela, Yossi Matias, Sotiris Nikoletseas, Wolfgang Thomas |

Publisher | Springer Berlin Heidelberg |

Pages | 127-138 |

Number of pages | 12 |

Volume | 5556 |

ISBN (Electronic) | 978-3-642-02930-1 |

ISBN (Print) | 978-3-642-02929-5 |

DOIs | |

Publication status | Published - 2009 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Berlin Heidelberg |