Qadratic Simulations of Merlin Arthur Games


The known proofs of MA C 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) C P-TIME (o(t2)). 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 Göös) that there is an oracle relative to which MA C NPBPP (which was previously known to hold by a proof using generics).

Publication Title

ACM Transactions on Computation Theory