This article shows that the universal generation problem for Optimality Theory (OT) is PSPACE-complete. While prior work has shown that universal generation is at least NP-hard and at most EXPSPACE-hard, 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 NP^NP-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 and NL-complete when the number of automata is bounded. 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.

本文表明，最优理论 (OT) 的通用生成问题是 PSPACE 完全的。虽然之前的工作表明通用生成至少是 NP 困难，最多是 EXPSPACE 困难，但我们的结果将通用生成置于这两个类之间，假设 NP ≠ PSPACE。我们还表明，当约束数量预先有界时，通用生成至少是 NL 困难，最多是 NP ^NP困难。我们的证明依赖于 OT 和有限自动机的交非空问题之间的紧密联系，一般来说是 PSPACE 完全的，当自动机的数量有界时是 NL 完全的。我们的分析表明，约束交互是造成 OT 复杂性的主要因素：将转换分解为简单的、交互约束的能力使 OT 能够对复杂的语音现象提供简洁的描述。