The complete classification for quantified equality constraints
Computational Complexity
2026-05-22 v3 Logic in Computer Science
Logic
Abstract
We prove that QCSP is PSpace-complete, settling a question open for more than ten years. This completes the complexity classification for the QCSP over equality languages as a trichotomy between Logspace, NP-complete and PSpace-complete. We additionally settle the classification for bounded alternation QCSP, for an equality language. Such problems are either in Logspace, NP-complete, co-NP-complete or rise in complexity in the Polynomial Hierarchy.
Cite
@article{arxiv.2104.00406,
title = {The complete classification for quantified equality constraints},
author = {Dmitriy Zhuk and Barnaby Martin and Michal Wrona},
journal= {arXiv preprint arXiv:2104.00406},
year = {2026}
}