computational complexity

, Volume 3, Issue 4, pp 307–318

BPP has subexponential time simulations unlessEXPTIME has publishable proofs

Authors

  • Lźszló Babai
    • Department of Computer ScienceUniversity of Chicago
  • Lance Fortnow
    • Department of Computer ScienceUniversity of Chicago
  • Noam Nisan
    • Department of Computer ScienceHebrew University
  • Avi Wigderson
    • Department of Computer ScienceHebrew University
Article

DOI: 10.1007/BF01275486

Cite this article as:
Babai, L., Fortnow, L., Nisan, N. et al. Comput Complexity (1993) 3: 307. doi:10.1007/BF01275486

Abstract

We show thatBPP can be simulated in subexponential time for infinitely many input lengths unless exponential time
  • ℴ collapses to the second level of the polynomial-time hierarchy.

  • ℴ has polynomial-size circuits and

  • ℴ has publishable proofs (EXPTIME=MA).

We also show thatBPP is contained in subexponential time unless exponential time has publishable proofs for infinitely many input lengths. In addition, we showBPP can be simulated in subexponential time for infinitely many input lengths unless there exist unary languages inMA-P.

The proofs are based on the recent characterization of the power of multiprover interactive protocols and on random self-reducibility via low-degree polynomials. They exhibit an interplay between Boolean circuit simulation, interactive proofs and classical complexity classes. An important feature of this proof is that it does not relativize.

One of the ingredients of our proof is a lemma that states that ifEXPTIME has polynomial size circuits thenEXPTIME=MA. This extends previous work by Albert Meyer.

Key words

Complexity ClassesInteractive Proof Systems

Subject classifications

68Q15

Copyright information

© Birkhäuser Verlag 1993