Disambiguation of Finite-State Transducers

Disambiguation of Finite-State Transducers N. Smaili and P. Cardinal and G. Boulianne and P. Dumouchel Centre de Recherche Informatique de Montr´eal. {nsmaili, pcardinal, gboulian, Pierre.Dumouchel}@crim.ca Abstract The objective of this work is to disambiguate transducers which have the following form: T = R ◦ D and to be able to apply the determinization algorithm described in (Mohri, 1997). Our approach to disambiguating T = R ◦ D consists first of computing the composition T and thereafter to disambiguate the transducer T. We will give an important consequence of this result that allows us to compose any number of transducers R with the transducer D, in contrast to the previous approach which consisted in first disambiguating transducers D and R to produce respectively D ′ and R ′, then computing T ′ = R ′ ◦D ′ where T ′ is unambiguous. We will present results in the case of a transducer D representing a dictionary and R representing phonological rules. Keywords: ambiguity, determinis- tic, dictionary, transducer. 1 Introduction The task of speech recognition can be decomposed into several steps, where each step is represented by a finite- state transducer (Mohri et al., 1998). The search space of the recognizer is defined by the composition of trans- ducers T = A ◦ C ◦ R ◦ D ◦ M. Trans- ducer A converts a sequence of obser- vations O to a sequence of context- dependent phones. ofTransducer C converts a sequence context-dependent phones to a sequence of context-independent phones. Transducer R is a mapping from phones to phones which imple- ments phonological rules. Transducer D is the pronunciations dictionary. It converts a sequence of context- independent phones to a sequence of words. Transducer M represents a language model: it converts sequences of words into sequences of words, while restricting the possible sequences or assigning a score to the sequences. The speech recognition problem con- sists of finding the path of least cost in transducer O ◦ T, where O is a sequence of acoustic observations. The pronunciations dictionary rep- resenting the mapping from pronun- ciations to words can show an inher- ent ambiguity: a sequence of phones can correspond to more than one word, so we cannot apply the transducer de- terminization algorithm (an operation which reduces the redundancy, search time and possibly space). This prob- lem is usually handled by adding spe- cial symbols to the dictionary to re- move the ambiguity in order to be able to apply the determinization al- gorithm (Koskenniemi, 1990). Never- theless, when we compose the dictio- nary with the phonological rules, we must take into account special sym- bols. This complicates the construc- tion of transducers representing these rules and leads to size explosion. would be simpler to compose the rulesIt with the dictionary, then remove the ambiguity in the result and then apply the determinization algorithm. 2 Notations and definitions Formally, a weighted transducer over a semiring K = (K, ⊕, ⊗, ¯0, ¯1) is defined as a 6-tuple T = (Q, I, …

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