BPP has subexponential time simulations unless EXPTIME has publishable proofs

It is shown that BPP can be simulated in subexponential time for infinitely many input lengths unless exponential time collapses to the second level of the polynomial-time hierarchy, has polynomial-size circuits, and has publishable proofs (EXPTIME=MA). It is also shown that BPP is contained in sube...

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Bibliographic Details
Published in[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference pp. 213 - 219
Main Authors Babai, L., Fortnow, L., Nisan, N., Wigderson, A.
Format Conference Proceeding
LanguageEnglish
Published IEEE Comput. Soc. Press 1991
Subjects
Circuit simulation
Computational modeling
Cryptography
Karhunen-Loeve transforms
Polynomials
Random number generation
Turing machines
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Summary:It is shown that BPP can be simulated in subexponential time for infinitely many input lengths unless exponential time collapses to the second level of the polynomial-time hierarchy, has polynomial-size circuits, and has publishable proofs (EXPTIME=MA). It is also shown that BPP is contained in subexponential time unless exponential time has publishable proofs for infinitely many input lengths. In addition, it is shown that 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.< >
ISBN:9780818622557
0818622555
DOI:10.1109/SCT.1991.160263