By maintaining these syntactic random variable stores, each hypothesis has access to the current language model probability for the partial translation ending at that hypothesis, as calculated by an incremental syntactic language model defined by the HHMM.
the random variable store at hypothesis h provides P(τ t h ) = P(e h 1..t , s 1..D 1..t ), where e h 1..t is the sequence of words in a partial hypothesis ending at h which contains t target words, and where there are D syntactic random variables in each random variable store (Eq.