BPP has subexponential time simulations unless EXPTIME has publishable proofs

Lźszló Babai*, Lance Fortnow, Noam Nisan, Avi Wigderson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

246 Scopus citations

Abstract

We show that BPP can be simulated in subexponential time for infinitely many input lengths unless exponential time{o script} collapses to the second level of the polynomial-time hierarchy. {o script} has polynomial-size circuits and {o script} has publishable proofs (EXPTIME=MA). We also show that BPP is contained in subexponential time unless exponential time has publishable proofs for infinitely many input lengths. In addition, we show BPP can be simulated in subexponential time for infinitely many input lengths unless there exist unary languages in MA-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 if EXPTIME has polynomial size circuits then EXPTIME=MA. This extends previous work by Albert Meyer.

Original languageAmerican English
Pages (from-to)307-318
Number of pages12
JournalComputational Complexity
Volume3
Issue number4
DOIs
StatePublished - Dec 1993

Keywords

  • Complexity Classes
  • Interactive Proof Systems
  • Subject classifications: 68Q15

Fingerprint

Dive into the research topics of 'BPP has subexponential time simulations unless EXPTIME has publishable proofs'. Together they form a unique fingerprint.

Cite this