The evaluation problem in discrete semi-hidden Markov models

This paper is devoted to discrete semi-hidden Markov models (SHMM), which are related to the well-known hidden Markov models (HMM). In particular, the HMM  associated to an SHMM  is defined, and the forward algorithm for solving the evaluation problem in SHMMs is introduced. Experiments show that in a set of randomly generated sequences with different SHMMs, the maximum value for the conditional probability of each sequence being generated by the model most frequently matches the model that generated the sequence. Something similar happens to associated HMMs, suggesting that the HMM  associated to a given SHMM  shows a certain affinity to this, which is higher than other HMMs.