Quadratic Simulations of Merlin-Arthur Games

The known proofs of MA. PP incur a quadratic overhead in the running time. We prove that this quadratic overhead is necessary for black-box simulations; in particular, we obtain an oracle relative to which MA-TIME(t) not subset of P-TIME(o(t(2))). We also show that 2-sided-error Merlin-Arthur games can be simulated by 1-sided-error Arthur-Merlin games with quadratic overhead. We also present a simple, query complexity based proof (provided by Mika Goos) that there is an oracle relative to which MA not subset of NPBPP (which was previously known to hold by a proof using generics).