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Quadratic Simulations of Merlin–Arthur Games

Published:03 May 2020Publication History
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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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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 12, Issue 2
      June 2020
      138 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/3382781
      Issue’s Table of Contents

      Copyright © 2020 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 3 May 2020
      • Accepted: 1 March 2020
      • Revised: 1 April 2019
      • Received: 1 December 2017
      Published in toct Volume 12, Issue 2

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