... constructing statistical lan-guage models. In Proceedings of the 41st AnnualMeeting of the Association for Computational Linguis-tics, pages 40–47.Cyril Allauzen, Michael Riley, Johan Schalkwyk, Woj-ciech ... possible. An exact encoding using other mecha-nisms is required in such cases to allow for off-linerepresentation and optimization. In this paper, we introduce a novel use of a semir-ing – the lexicographic ... epsilon approximation, this semiring al-lows for an exact representation, while also allow-ing (unlike failure transition approaches) for off-linecomposition with other transducers, with all...