Optimality Theory and the Generative Complexity of Contraint Violability

Analyses within generative phonology have traditionally been stated in terms of systems of rewrite rules, which, when applied in the appropriate sequence, produce from an underlying representation the appropriate surface form. This view of phonological analysis has been adopted in almost all work in computational phonology, where the goal has been to produce feasible implementations of phonological rule systems for use in generating surface forms from lexical specifications as well as in parsing surface forms into underlying representations. As first pointed out by Johnson (1972), the effects of phonological rewrite rules can be simulated using only finite state machinery, with iterative application accomplished by sending the output from one transducer to the input of the next, a process which can be compiled out into a single transducer so as to apply in time linear in the length of the string, but independent of the number and complexity of the rules. Consequently, since the pioneering work by Kaplan and Kay (1994) and Koskenniemi (1984), computational implementations of phonological rule systems have been done using finite state transducers or extensions thereof (Kornai 1991; Wiebe 1992). Recently, there has been a shift in focus in much of the work on phonological theory, from systems of rules to sets of constraints on well-formedness (Paradis 1988, Scobbie 1991, Prince and Smolensky 1993, Burzio 1994, Bird and Klein 1994, inter alia). This shift has, however, had relatively little impact upon computational work (but see Bird and Ellison 1994). In this paper, we begin an examination of the effects of the move from rule-based to constraint-based theories upon the generative properties of phonological theories. Specifically, we will focus our efforts on the issue of whether the widely adopted constraint-based view known as Optimality Theory (OT) may be instantiated in a finite state transducer. OT raises a particularly interesting theoretical question in this context: it allows the specification of a ranking among the constraints and allows