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International Workshop on Coalgebraic Methods in Computer Science

CMCS 2012: Coalgebraic Methods in Computer Science pp 71–89Cite as

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Structural Operational Semantics for Continuous State Probabilistic Processes

Structural Operational Semantics for Continuous State Probabilistic Processes

  • Giorgio Bacci18 &
  • Marino Miculan18 
  • Conference paper
  • 578 Accesses

  • 3 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7399)

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.

Keywords

  • Measurable Space
  • Natural Transformation
  • Initial Sequence
  • Label Transition System
  • Measure Term

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Work supported by MIUR PRIN project 20088HXMYN, “SisteR”.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Computer Science, University of Udine, Italy

    Giorgio Bacci & Marino Miculan

Authors
  1. Giorgio Bacci
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  2. Marino Miculan
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Editor information

Editors and Affiliations

  1. Research School of Information Sciences and Engineering, The Australian National University, 0200, Canberra, ACT, Australia

    Dirk Pattinson

  2. Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany

    Lutz Schröder

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Bacci, G., Miculan, M. (2012). Structural Operational Semantics for Continuous State Probabilistic Processes. In: Pattinson, D., Schröder, L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32784-1_5

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