Representation of Markov's chains functions over finite field based on stochastic matrix lumpability

Abstract

A polynomial model of functions of lumped Markov's chains over finite field is represented. The authors represent a particular case of Markov's chains functions &#x2014; the hidden Markov's models (HMM). A definition of the HMM stochastic equivalency was implemented based on stochastic matrix lumpability and asymptotic characteristics of HMM. The paper provides a polynomial representation of an equivalent HMM over the finite field GF(2<sup>n</sup>). It estimates a minimal order of the field GF(2<sup>n</sup>) for polynomial HMM representation, depending on the stochastic matrices implying vector size and possessing lumpability characteristic.

Cite this paper

@article{Zakharov2016RepresentationOM, title={Representation of Markov's chains functions over finite field based on stochastic matrix lumpability}, author={Valery M. Zakharov and B. F. Eminov and S. V. Shalagin}, journal={2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)}, year={2016}, pages={1-5} }