Universal Generation for Optimality Theory Is PSPACE-Complete

This paper shows that the universal generation problem (Heinz, Kobele, and Riggle 2009) for Optimality Theory (OT, Prince and Smolensky 1993, 2004) is PSPACE-complete. While prior work has shown that universal generation is at least NP-hard (Eisner 1997, 2000b; Wareham 1998; Idsardi 2006) and at most EXPSPACE-hard (Riggle 2004), our results place universal generation in between those two classes, assuming that NP ≠ PSPACE. We additionally show that when the number of constraints is bounded in advance, universal generation is at least NL-hard and at most NPNP-hard. Our proofs rely on a close connection between OT and the intersection non-emptiness problem for finite automata, which is PSPACE-complete in general (Kozen 1977) and NL-complete when the number of automata is bounded (Jones 1975). Our analysis shows that constraint interaction is the main contributor to the complexity of OT: the ability to factor transformations into simple, interacting constraints allows OT to furnish compact descriptions of intricate phonological phenomena.