We study some problems solvable in deterministic polynomial time given oracle access to the (promise version of) the Arthur-Merlin class.
Our main results are the following: (i) $BPP^{NP}_{||} \subseteq P^{prAM}_{||}$; (ii) $S_2^p \subseteq P^{prAM}$. In addition to providing new upperbounds for the classes $S_2^p$ and $BPP^{NP}_{||}$, these results are interesting ... more >>>

Korten and Pitassi (FOCS, 2024) defined a new complexity class $L_2P$ as the polynomial-time Turing closure of the Linear Ordering Principle. They put it between $MA$ (Merlin--Arthur protocols) and $S_2P$ (the second symmetric level of the polynomial hierarchy).

In this paper we sandwich $L_2P$ between $P^{prMA}$ and $P^{prSBP}$. (The oracles ... more >>>