WFST

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Introduction

Finite State Transducer

6 tuple: \(FST = (Q, \Sigma, \Delta, E, I, F)\) - \(Q\): finite set of states - \(\Sigma\): finite set of input symbols - \(\Delta\): finite set of output symbols - \(E\): set of transitions - \(I\): initial state - \(F\): set of final states

WFST is a generalization of FST, with weights on transitions and states. It is a directed graph with states as nodes and transitions as edges. Each transition has an input label, an output label, and a weight. The weight is a semiring element, which is a generalization of the real number. The semiring element is used to represent the cost of the transition. The weight of a path is the sum of the weights of the transitions on the path. The weight of a path is used to represent the cost of the path.