Logic and model checking for hidden markov models

Authors:
Lijun Zhang;Holger Hermanns;David N. Jansen
Affiliations:
Department of Computer Science, Saarland University, Saarbrücken, Germany;Department of Computer Science, Saarland University, Saarbrücken, Germany;Department of Computer Science, University of Twente, Enschede, The Netherlands
Venue:
FORTE'05 Proceedings of the 25th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
Year:
2005

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Abstract

The branching-time temporal logic PCTL* has been intro- duced to specify quantitative properties over probability systems, such as discrete-time Markov chains. Until now, however, no logics have been defined to specify properties over hidden Markov models (HMMs). In HMMs the states are hidden, and the hidden processes produce a se- quence of observations. In this paper we extend the logic PCTL* to POCTL*. With our logic one can state properties such as “there is at least a 90 percent probability that the model produces a given sequence of observations” over HMMs. Subsequently, we give model checking algorithms for POCTL* over HMMs.