, Volume 3, Issue 4, pp 307318
First online:
BPP has subexponential time simulations unlessEXPTIME has publishable proofs
 Lźszló BabaiAffiliated withDepartment of Computer Science, University of Chicago
 , Lance FortnowAffiliated withDepartment of Computer Science, University of Chicago
 , Noam NisanAffiliated withDepartment of Computer Science, Hebrew University
 , Avi WigdersonAffiliated withDepartment of Computer Science, Hebrew University
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Get AccessAbstract

ℴ collapses to the second level of the polynomialtime hierarchy.

ℴ has polynomialsize 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 inMAP.
The proofs are based on the recent characterization of the power of multiprover interactive protocols and on random selfreducibility via lowdegree 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 Classes Interactive Proof SystemsSubject classifications
68Q15 Title
 BPP has subexponential time simulations unlessEXPTIME has publishable proofs
 Journal

computational complexity
Volume 3, Issue 4 , pp 307318
 Cover Date
 199312
 DOI
 10.1007/BF01275486
 Print ISSN
 10163328
 Online ISSN
 14208954
 Publisher
 BirkhäuserVerlag
 Additional Links
 Topics
 Keywords

 Complexity Classes
 Interactive Proof Systems
 68Q15
 Industry Sectors
 Authors

 Lźszló Babai ^{(1)}
 Lance Fortnow ^{(1)}
 Noam Nisan ^{(2)}
 Avi Wigderson ^{(2)}
 Author Affiliations

 1. Department of Computer Science, University of Chicago, 60637, Chicago, IL, USA
 2. Department of Computer Science, Hebrew University, Jerusalem, Israel