In view of objectively-existing forward and backward contextual dependent information in speech signal

in this paper we show that a conditional probability can be used to explicitly express these information in speech signal

which is called Forward and Backward Markov Contextual Dependences. And the Forward and Backward Hidden Markov Models

which are believed to contain these two Markov Contextual Dependences respectively

are also presented here. Our experimental results prove that we can obtain the relatively acceptable performance in speech recognition only using the Backward Markov Contextual Dependence. It is at least comparable with the recognition performance obtained from normal forward HMM with Forward Markov Contextual Dependence. In this paper

we also study the methods of simutaneously taking advantages of these two Markov Contextual Dependences of speech in isolated word recognition and continuous speech recognition respectively

and propose an effective algorithm in continuous speech recognition-Forward and Backward Mixed Bisected Search（FBMBS）

which can utilize the immediate results of Forward HMM based forward Viterbi search and Backward HMM based backward Viterbi search

so that we can conveniently combine these two Markov Contextual Dependences in continuous speech recognition at the same time. Our experiments show that the FBMBS algorithm really is consistently superior to that of using either of these two Contextual Dependences alone.