Composition and Weight Pushing of Monotonic Subsequential Failure Transducers Representing Probabilistic Models

We present a construction for the composition of subsequential transducers (representing conditional probabilistic models) with subsequential failure transducers (representing probabilistic models). Under certain conditions, satisfied by the corresponding transduction devices, a more efficient construction is applicable that avoids the creation of unnecessary states. Furthermore, the weights of the resulting failure transducers can be efficiently redistributed via weight pushing in the $\langle \mathbb{R}_+, +, \times, 0, 1 \rangle$ and $\langle \mathbb{R}_+, \max, \times, 0, 1 \rangle$ semirings.