### Finding Irrefutable Certificates for S_2^p via Arthur and Merlin

Venkatesan T. Chakaravarthy & Sambuddha Roy
We show that $S_2^psubseteq P^{prAM}$, where $S_2^p$ is the symmetric alternation class and $prAM$ refers to the promise version of the Arthur-Merlin class $AM$. This is derived as a consequence of our main result that presents an $FP^{prAM}$ algorithm for finding a small set of collectively irrefutable certificates'' of a given $S_2$-type matrix. The main result also yields some new consequences of the hypothesis that $NP$ has polynomial size circuits. It is known that the...