Strictness of ACC^0 versus TC^0

Prove or refute the strict inclusion ACC^0 ⊊ TC^0.

Background

The paper records that ACC0 is contained in TC0 and that the inclusion is widely believed to be strict. However, the strictness has not been established, so determining whether threshold gates provide strictly greater power than bounded-modulus counting gates remains an unresolved classical circuit-complexity problem.

This question is also relevant to the paper’s exact-QAC0 separation results, which show that EQAC0 is not contained in ACC0 under the assumption that ACC0 is strictly contained in TC0.

References

While it is widely believed that this inclusion is strict, it is yet to be proven.

— The Robustness of QAC0  (2610.02154 - Grier et al., 1 Oct 2026) in Section 2, “Classical circuit complexity”