Rational Transductions for Phonetic Conversion and Phonology

33 than for French, and since BiPho makes only minimal assumptions about the mathematical properties of the conversion, we believe that it can be used for virtually any conversion task related to phonetics. Koskenniemi, Kimmo. 1983. Two-level morphology: a general computational model for word-form recognition and production. Publication no. 11. 32 ble whose rows are indexed by left-to-right states and whose lines are indexed by right-to-left states. The content of the table at line ! q and at column q is a key that gives access to the set left(! q) \ right(q). Output is a two-dimensional table whose rows are indexed by the keys of the sets left(! q) \ right(q), and whose lines are indexed by input symbols. The content of the table at line k and at column a is the output sequence (! q ; a; q) deened in section 6.2. 6.3 Running the bimachine When running the bimachine on an input string, the string is rst processed in reverse order: we compute the values of the states of the right-to-left automaton for each symbol in the input string and store them in a one-dimensional array. Then, for each symbol from left to right, the state of the left-to-right automaton is computed. This value is used with the value of the right-to-left state, the input symbol and the tables BimSet and Output in order to retrieve the output sequence. The complexity of this algorithm is independent of the number of states and transitions of the bimachine: the time of the conversion is dominated by the length of the input sequence. 7 Conclusion The nite-state formal devices described in this chapter and tested in the context of phonetics and phonology proved to be both convenient for linguistic description and adapted for eecient implementation. The conversion system BiPho was tested with complete phonetic conversion data for French. Since phonetic conversion of most languages is simpler 31 u y 00 p t k b d g f s M v z `