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) ⊈ 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⊈ NPBPP (which was previously known to hold by a proof using generics).

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)