Back in 2007-2008 Mehryar Mohri ,Fernando Pereira and Google researcher Michael Riley, were developing speech recognition system based on Weighted Finite State Transducer.The transducer proposed by them provided a common and natural representation for major components of speech recognition systems, including hidden Markov models (HMMs), context-dependency models, pronunciation dictionaries, statistical grammars, and word or phone lattices.[1]

A finite-state transducer is a finite automaton whose state transitions are labeled with both input and output symbols while a weighted transducer puts weights on transitions in addition to the input and output symbols.[1] The examples in Figure 1(a) [1, Fig.1] represents the language model used for speech recognition by giving each transition identical input and output labels. This language model predicts how probable particular sentence over other. For example, if the first is ‘using’ (having probability of occurrence 1) then the word following it can be either ‘data’ with probability of occurrence 0.66...