Quadratic simulations of Merlin–Arthur games
Abstract
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)
Recommended Citation
Watson, T. (2018). Quadratic simulations of Merlin–Arthur games. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10807 LNCS, 864-872. https://doi.org/10.1007/978-3-319-77404-6_62
