IP = PSPACE

@article{Shamir1992IPP,
  title={IP = PSPACE},
  author={Adi Shamir},
  journal={J. ACM},
  year={1992},
  volume={39},
  pages={869-877}
}
  • A. Shamir
  • Published 1 October 1992
  • Mathematics
  • J. ACM
In this paper, it is proven that when both randomization and interaction are allowed, the proofs that can be verified in polynomial time are exactly those proofs that can be generated with polynomial space. 
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A slightly simplified version of Shamir's proof is presented, using degree reductions instead of simple QBFs, to prove that PH is contained in IP.
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How the major computational complexity classes, P, NP and PSPACE, capture different computational properties of mathematical proofs and reveal new quantitative aspects of mathematics are discussed.
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More on BPP and the Polynomial-Time Hierarchy
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  • Mathematics, Computer Science
    Inf. Process. Lett.
  • 1996
Progress on Polynomial Identity Testing - II
  • Nitin Saxena
  • Mathematics
    Electron. Colloquium Comput. Complex.
  • 2013
TLDR
The area of algebraic complexity theory is surveyed, with the focus being on the problem of polynomial identity testing (PIT), and the key ideas are discussed.
On Random Oracle Separations
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This technique is used to prove that every language in the polynomial-time hierarchy has an interactive proof system and played a pivotal role in the recent proofs that IP = PSPACE and MIP = NEXP.
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Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage. rhe ACM copyright notice and the title of
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