Universal Generation for Optimality Theory Is PSPACE-Complete

Sophie Hao


Abstract
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 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 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.
Anthology ID:
2024.cl-1.4
Volume:
Computational Linguistics, Volume 50, Issue 1 - March 2024
Month:
March
Year:
2024
Address:
Cambridge, MA
Venue:
CL
SIG:
Publisher:
MIT Press
Note:
Pages:
83–117
Language:
URL:
https://aclanthology.org/2024.cl-1.4
DOI:
10.1162/coli_a_00494
Bibkey:
Cite (ACL):
Sophie Hao. 2024. Universal Generation for Optimality Theory Is PSPACE-Complete. Computational Linguistics, 50(1):83–117.
Cite (Informal):
Universal Generation for Optimality Theory Is PSPACE-Complete (Hao, CL 2024)
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PDF:
https://aclanthology.org/2024.cl-1.4.pdf