Results 1  10
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1,567
On The BPP Hierarchy Problem
, 1997
"... In this paper we give arguments both for and against the existence of an oracle A, relative to which BPP equals probabilistic linear time. First, we prove a structure theorem for probabilistic oracle machines, which says that either we can fix the output of the machine by setting the answer to only ..."
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Cited by 2 (0 self)
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. Thus the question whether probabilistic polynomial time has a hierarchy relative to all oracles remains completely open.
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
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Cited by 2837 (11 self)
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We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a
Symmetric alternation captures BPP
, 1995
"... We introduce the natural class SP 2 containing those languages which maybe exP pressed in terms of two symmetric quanti ers. This class lies between 2 and P 2 \ P 2 and naturally generates a \symmetric " hierarchy corresponding to the polynomialtime hierarchy. Wedemonstrate, using the probabi ..."
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Cited by 49 (1 self)
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We introduce the natural class SP 2 containing those languages which maybe exP pressed in terms of two symmetric quanti ers. This class lies between 2 and P 2 \ P 2 and naturally generates a \symmetric " hierarchy corresponding to the polynomialtime hierarchy. Wedemonstrate, using
Towards NEXP versus BPP?
"... Abstract. We outline two plausible approaches to improving the miserable state of affairs regarding lower bounds against probabilistic polynomial time (namely, the class BPP). 1 ..."
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Abstract. We outline two plausible approaches to improving the miserable state of affairs regarding lower bounds against probabilistic polynomial time (namely, the class BPP). 1
In a World of P=BPP
, 2010
"... We show that proving results such as BPP = P essentially necessitate the construction of suitable pseudorandom generators (i.e., generators that suffice for such derandomization results). In particular, the main incarnation of this equivalence refers to the standard notion of uniform derandomization ..."
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decade or so (starting with Impagliazzo and Wigderson [JCSS, 2001]). We also identify a natural class of search problems that can be solved by deterministic polynomialtime reductions to BPP. This result is instrumental to the construction of the aforementioned pseudorandom generators (based
On reachability equivalence for BPPnets
 Theoretical Computer Science
, 1996
"... In this paper, we study the complexity of the reachability equivalence problem for BPPnets. BPPnets are closely related to Basic Parallel Processes, which form a subclass of Milner's CCS. We show the reachability equivalence problem for BPP nets to be solvable in DT!ME(22A), where d is a co ..."
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Cited by 6 (3 self)
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In this paper, we study the complexity of the reachability equivalence problem for BPPnets. BPPnets are closely related to Basic Parallel Processes, which form a subclass of Milner's CCS. We show the reachability equivalence problem for BPP nets to be solvable in DT!ME(22A), where d is a
Another proof that BPP ⊆ PH (and more
, 1997
"... Abstract. We provide another proof of the Sipser–Lautemann Theorem by which BPP ⊆ MA ( ⊆ PH). The current proof is based on strong results regarding the amplification of BPP, due to Zuckerman (1996). Given these results, the current proof is even simpler than previous ones. Furthermore, extending th ..."
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Cited by 28 (2 self)
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the proof leads to two results regarding MA: MA ⊆ ZPP N P (which seems to be new), and that twosided error MA equals MA. Finally, we survey the known facts regarding the fragment of the polynomialtime hierarchy that contains MA.
BPP has Subexponential Time Simulations unless EXPTIME has Publishable Proofs (Extended Abstract)
, 1993
"... ) L'aszl'o Babai Noam Nisan y Lance Fortnow z Avi Wigderson University of Chicago Hebrew University Abstract We show that BPP can be simulated in subexponential time for infinitely many input lengths unless exponential time ffl collapses to the second level of the polynomialtime ..."
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Cited by 111 (9 self)
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time hierarchy, ffl has polynomialsize circuits and ffl 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
Relativized Perfect ZeroKnowledge is not BPP
 INFORMATION AND COMPUTATION
, 1991
"... In this paper we further study the complexity of of zeroknowledge interactive proofs. We prove that there is an oracle A such that there is a language L which is recognizable by a two round, perfect zeroknowledge interactive proof relative to A, but such that L 62 BPP A. This gives interesting i ..."
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Cited by 4 (0 self)
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In this paper we further study the complexity of of zeroknowledge interactive proofs. We prove that there is an oracle A such that there is a language L which is recognizable by a two round, perfect zeroknowledge interactive proof relative to A, but such that L 62 BPP A. This gives interesting
Results 1  10
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1,567