The complete classification for quantified equality constraints
Dmitriy N. Zhuk, Barnaby D. Martin, Michał Wrona · Society for Industrial and Applied Mathematics eBooks · 2023
We prove that QCSP(ℕ; x = y → y = z) 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(Γ), for Γ an equality language. Such problems are either in Logspace, NP-complete, co-NP-complete or rise in complexity in the Polynomial Hierarchy.