Nonconcatenative Finite-State Morphology

In the last few years, so called finite.state morphology, in general, and two-level morphology in particular, have become widely accepted as paradigms for the computational t reatment of morphology. Finite-state morphology appeals to the notion of a finite-state transducer, which is simply a classical finite-state automaton whose transitions are labeled with pairs, rather than with single symbols. The automaton operates on a pair of tapes and advances over a given transition if the current symbols on the tapes match the pair on the transition. One member of the pair of symbols on a transition can be the designated null symbol, which we will write ~. When this appears, the corresponding tape is not examined, and it does not advance as the machine moves to the next state. Finite-state morphology originally arose out of a desire to provide ways of analyzing surface forms using grammars expressed in terms of systems of ordered rewriting rules. Kaplan and Kay (in preparation} observed, that finite-state transducers could be used to mimic a large class of rewriting rules, possibly including all those required for phonology. The importance ,ff this came from two considerations. First, transducers are indifferent as to the direction in which they are applied. In other words, they can be used with equal facility to translate between tapes, in either direction, to accept or reject pairs of tapes, or to generate pairs of tapes. Second, a pair of transducers with one tape in common is equivalent to a single transducer operating on the remaining pair of tapes. A simple algorithm exists for constructing the transition diagram fi)r this composite machine given those of the origihal pair. By repeated application of this algorithm, it is therefore possible to reduce a cascade of transducers, each linked to the next by a common tape, to a .~ingie transducer which accepts exactly the same pair of tapes as was accepted by the original cascade as a whole. From these two facts together, it follows that an arbi trary ordered set of rewrit ing rules can be modeled by a finite-state transducer which can be automatical ly constructed from them and which serves as well for analyzing surface forms as for generating them from underlying lexical strings. A transducer obtained from an ordered set of rules in the way just outlined is a two level device in the sense that it mediates directly between lexical and surface forms without ever constructing the intermediate forms that would arise in the course of applying the original rules one by one. The term two-level morphology, however, is used in a more restricted way, to apply to a system in which no intermediate forms are posited, even in the original grammatical formalism. The writer of a grammar using a two-level formalism never needs to think in terms of any representations other than the lexical and the surface ones. What he does is to specify, using one formalism or another, a set of transducers, each of which mediates directly between these fol'ms and each of which restricts the allowable pairs of strings in some way. The pairs that the system as a whole accepts are those are those that ~lre rejected by none of the component transducers, modulo certain assumptions about the precise way in which they interact, whose details need not concern us. Once again, there is a formal procedure that can be used to combine the set of transducers that make up such a system