## Abstract

We consider the problem of modeling syntax and semantics of probabilistic processes with continuous states (e.g. with continuous data). Syntax and semantics of these systems can be defined as algebras and coalgebras of suitable endofunctors over Meas, the category of measurable spaces. In order to give a more concrete representation for these coalgebras, we present an SOS-like rule format which induces an abstract GSOS over Meas; this format is proved to yield a fully abstract universal semantics, for which behavioural equivalence is a congruence.

To this end, we solve several problems. In particular, the format has to specify how to compose the semantics of processes (which basically are continuous state Markov processes). This is achieved by defining a language of measure terms, i.e., expressions specifically designed for describing probabilistic measures. Thus, the transition relation associates processes with measure terms.

As an example application, we model a CCS-like calculus of processes placed in an Euclidean space. The approach we follow in this case can be readily adapted to other quantitative aspects, e.g. Quality of Service, physical and chemical parameters in biological systems, etc.

To this end, we solve several problems. In particular, the format has to specify how to compose the semantics of processes (which basically are continuous state Markov processes). This is achieved by defining a language of measure terms, i.e., expressions specifically designed for describing probabilistic measures. Thus, the transition relation associates processes with measure terms.

As an example application, we model a CCS-like calculus of processes placed in an Euclidean space. The approach we follow in this case can be readily adapted to other quantitative aspects, e.g. Quality of Service, physical and chemical parameters in biological systems, etc.

Original language | English |
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Book series | Lecture Notes in Computer Science |

Volume | 7399 |

Pages (from-to) | 71-89 |

ISSN | 0302-9743 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

Event | Workshop on Coalgebraic Methods in Computer Science - Tallinn, Estonia Duration: 31 Mar 2012 → 1 Apr 2012 Conference number: 11 |

### Workshop

Workshop | Workshop on Coalgebraic Methods in Computer Science |
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Number | 11 |

Country/Territory | Estonia |

City | Tallinn |

Period | 31/03/2012 → 01/04/2012 |