Belief Bisimulation for Hidden Markov Models

Logical Characterisation and Decision Algorithm
  • David N. Jansen
  • Flemming Nielson
  • Lijun Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7226)

Abstract

This paper establishes connections between logical equivalences and bisimulation relations for hidden Markov models (HMM). Both standard and belief state bisimulations are considered.

We also present decision algorithms for the bisimilarities. For standard bisimilarity, an extension of the usual partition refinement algorithm is enough. Belief bisimilarity, being a relation on the continuous space of belief states, cannot be described directly. Instead, we show how to generate a linear equation system in time cubic in the number of states.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • David N. Jansen
    • 1
  • Flemming Nielson
    • 2
  • Lijun Zhang
    • 2
  1. 1.Radboud Universiteit NijmegenThe Netherlands
  2. 2.Technical University of DenmarkDenmark

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