This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general subshift over usually an uncountable alphabet. It is shown that at most the second order representation is enough for a continuous map. In particular, it is shown...

This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general subshift over usually an uncountable alphabet. It is shown that at most the second order representation is enough for a continuous map. In particular, it is shown...

It is well known that in an o-minimal hybrid system the continuous and discrete components can be separated, and therefore the problem of finite bisimulation reduces to the same problem for a transition system associated with a continuous dynamical system. It was recently proved by several authors that under certain natural assumptions such finite bisimulation exists. In the paper we consider o...

Compared to fully-continuous HMMs, semi-continuous HMMs are more compact in size, require less data to train well and result in comparable recognition performance with much faster decoding speeds. Nevertheless, the use of semi-continuous HMMs in large vocabulary speech recognition systems has declined considerably in recent years. A significant factor that has contributed this is that systems t...

In this work the output density functions of hidden Markov models are phoneme-wise tied mixture Gaussians. For training these tied mixture density HMMs, modiied versions of the Viterbi training and LVQ based corrective tuning are described. The initialization of the mean vectors of the mixture Gaussians is performed by rst composing small Self-Organizing Maps representing each phoneme and then ...