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The Untold Story of \(\mathsf {SBP}\)

  • Ilya VolkovichEmail author
Conference paper
  • 70 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12159)

Abstract

In the seminal work of [4], Babai has introduced Arthur-Merlin Protocols and in particular the complexity classes \(\mathsf {MA}\) and \(\mathsf {AM}\) as randomized extensions of the class \(\mathsf {NP}\). While it is easy to see that \(\mathsf {NP}\subseteq \mathsf {MA}\subseteq \mathsf {AM}\), it has been a long standing open question whether these classes are actually different. In [5], Böhler et al. introduced the probabilistic class of \(\mathsf {SBP}\) and showed that \(\mathsf {MA}\subseteq \mathsf {SBP}\subseteq \mathsf {AM}\). Indeed, this is the only known natural complexity class that lies between \(\mathsf {MA}\) and \(\mathsf {AM}\). In this work we study the relations between these classes further, partially answering some open questions posed in [5].

Keywords

Arthur-Merlin Protocols Randomized complexity theory \(\mathsf {NP}\) problems with bounded number of solutions \(\mathsf {SZK}\) 

Notes

Acknowledgment

The author would like to extend his gratitude to Thomas Watson and Ryan Williams for useful conversations. Finally, the author would like to thank Henning Fernau and the anonymous referees for their detailed comments and suggestions.

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Authors and Affiliations

  1. 1.CSE DivisionUniversity of MichiganAnn ArborUSA

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