Quadratic Simulations of Merlin–Arthur Games
Article No.: 14, Pages 1 - 11
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).
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Index Terms
- Quadratic Simulations of Merlin–Arthur Games
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June 2020
138 pages
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Publication History
Published: 03 May 2020
Accepted: 01 March 2020
Revised: 01 April 2019
Received: 01 December 2017
Published in TOCT Volume 12, Issue 2
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