Adapting arguments from Eisner 1997, 2000, this remark provides a simple proof that the generation problem for Optimality Theory (Prince and Smolensky 2004) is NP-hard. The proof needs only the binary evaluation of constraints and uses only constraints generally employed in the Optimality Theory literature. In contrast, rule-based derivational systems are easily computable, belonging to the class of polynomialtime algorithms, P (Eisner 2000).

Chomsky (1995) cites Hebrew spirantization as an example of a phonological phenomenon whose conditioning factors are rendered opaque by the operation of later processes in the phonological derivation. Because Optimality Theory (OT; e.g., Prince and Smolensky 1993) is built on surface output conditions (and in more recent versions constraints comparing input and output representations and enforcing uniformity in paradigms), any such cases of intermediate representations raise nontrivial questions for OT. These cases become more interesting and revealing when we try to provide comprehensive OT accounts using the general devices employed in the OT literature. This article examines Tiberian Hebrew spirantization in greater detail and demonstrates that spirantization and related phenomena cannot be adequately handled nonderivationally in OT.