Phonological Comprehension and the Compilation of Optimality Theory

Comprehension and Compilation in Optimality Theory∗ Jason Eisner Department of Computer Science Johns Hopkins University Baltimore, MD, USA 21218-2691 jason@cs.jhu.edu Abstract This paper ties up some loose ends in finite-state Optimality Theory. First, it discusses how to perform comprehension un- der Optimality Theory grammars consisting of finite-state con- straints. Comprehension has not been much studied in OT; we show that unlike production, it does not always yield a regular set, making finite-state methods inapplicable. However, after giving a suitably flexible presentation of OT, we show care- fully how to treat comprehension under recent variants of OT in which grammars can be compiled into finite-state transduc- ers. We then unify these variants, showing that compilation is possible if all components of the grammar are regular relations, including the harmony ordering on scored candidates. A side benefit of our construction is a far simpler implementation of directional OT (Eisner, 2000). 1 Introduction To produce language is to convert utterances from their underlying (“deep”) form to a surface form. Optimality Theory or OT (Prince and Smolensky, 1993) proposes to describe phonological production as an optimization process. For an underlying x, a speaker purportedly chooses the surface form z so as to maximize the harmony of the pair (x, z). Broadly speaking, (x, z) is harmonic if z is “easy” to pronounce and “similar” to x. But the precise har- mony measure depends on the language; according to OT, it can be specified by a grammar of ranked desiderata known as constraints. According to OT, then, production maps each un- derlying form to its best possible surface pronuncia- tion. It is akin to the function that maps each child x to his or her most flattering outfit z. Different chil- dren look best in different clothes, and for an oddly shaped child x, even the best conceivable outfit z may be an awkward compromise between style and fit—that is, between ease of pronunciation and sim- ilarity to x. Language comprehension is production in re- verse. In OT, it maps each outfit z to the set of chil- ∗Thanks to Kie Zuraw for asking about comprehension; to Ron Kaplan for demanding an algebraic construction before he believed directional OT was finite-state; and to others whose questions convinced me that this paper deserved to be written. dren x for whom that outfit is optimal, i.e., is at least as flattering as any other outfit z′: PRODUCE(x) = {z : (∄z′) (x, z′) > (x, z)} COMPREHEND(z) = {x : z ∈ PRODUCE(x)} = {x : (∄z′) (x, z′) > (x, z)} In general z and z′ may range over infinitely many possible pronunciations. While the formulas above are almost identical, comprehension is in a sense more complex because it varies both the underlying and surface forms. While PRODUCE(x) considers all pairs (x, z′), COMPREHEND(z) must for each x consider all pairs (x, z′). Of course, this nested def- inition does not preclude computational shortcuts. This paper has three modest goals: 1. To show that OT comprehension …

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