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Electronic Colloquium on Computational Complexity

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Reports tagged with BPP:
TR97-045 | 29th September 1997
Oded Goldreich, David Zuckerman

Another proof that BPP subseteq PH (and more).

Comments: 1

We provide another proof of the Sipser--Lautemann Theorem
by which $BPP\subseteq MA$ ($\subseteq PH$).
The current proof is based on strong
results regarding the amplification of $BPP$, due to Zuckerman.
Given these results, the current proof is even simpler than previous ones.
Furthermore, extending the proof leads ... more >>>

TR02-039 | 30th June 2002
Oded Goldreich, Avi Wigderson

Derandomization that is rarely wrong from short advice that is typically good

Comments: 1

For every $\epsilon>0$,
we present a {\em deterministic}\/ log-space algorithm
that correctly decides undirected graph connectivity
on all but at most $2^{n^\epsilon}$ of the $n$-vertex graphs.
The same holds for every problem in Symmetric Log-space (i.e., $\SL$).

Making no assumptions (and in particular not assuming the ... more >>>

TR02-055 | 13th September 2002
Valentine Kabanets, Russell Impagliazzo

Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds

Revisions: 1

We show that derandomizing Polynomial Identity Testing is,
essentially, equivalent to proving circuit lower bounds for
NEXP. More precisely, we prove that if one can test in polynomial
time (or, even, nondeterministic subexponential time, infinitely
often) whether a given arithmetic circuit over integers computes an
identically zero polynomial, then either ... more >>>

TR05-018 | 6th February 2005
Oded Goldreich

On Promise Problems (a survey in memory of Shimon Even [1935-2004])

The notion of promise problems was introduced and initially studied
by Even, Selman and Yacobi
(Information and Control, Vol.~61, pages 159-173, 1984).
In this article we survey some of the applications that this
notion has found in the twenty years that elapsed.
These include the notion ... more >>>

TR05-037 | 8th April 2005
Eric Allender, Peter B├╝rgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen

On the Complexity of Numerical Analysis

Revisions: 1 , Comments: 1

We study two quite different approaches to understanding the complexity
of fundamental problems in numerical analysis. We show that both hinge
on the question of understanding the complexity of the following problem,
which we call PosSLP:
Given a division-free straight-line program
producing an integer N, decide whether N>0.
more >>>

TR05-137 | 21st November 2005
Emanuele Viola

On Probabilistic Time versus Alternating Time

We prove several new results regarding the relationship between probabilistic time, BPTime(t), and alternating time, \Sigma_{O(1)} Time(t). Our main results are the following:

1) We prove that BPTime(t) \subseteq \Sigma_3 Time(t polylog(t)). Previous results show that BPTime(t) \subseteq \Sigma_2 Time(t^2 log t) (Sipser and Gacs, STOC '83; Lautemann, IPL '83) ... more >>>

TR08-073 | 4th August 2008
Dmitry Itsykson

Structural complexity of AvgBPP

We study class AvgBPP that consists of distributional problems that can be solved in average polynomial time (in terms of Levin's average-case complexity) by randomized algorithms with bounded error. We prove that there exists a distributional problem that is complete for AvgBPP under polynomial-time samplable distributions. Since we use deterministic ... more >>>

TR12-028 | 30th March 2012
Eric Allender, George Davie, Luke Friedman, Samuel Hopkins, Iddo Tzameret

Kolmogorov Complexity, Circuits, and the Strength of Formal Theories of Arithmetic

Revisions: 1

Can complexity classes be characterized in terms of efficient reducibility to the (undecidable) set of Kolmogorov-random strings? Although this might seem improbable, a series of papers has recently provided evidence that this may be the case. In particular, it is known that there is a class of problems $C$ defined ... more >>>

TR12-054 | 2nd May 2012
Eric Allender, Harry Buhrman, Luke Friedman, Bruno Loff

Reductions to the set of random strings:the resource-bounded case

Revisions: 1

This paper is motivated by a conjecture that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out by [Allender et al] to settle this conjecture cannot succeed without significant alteration, but that it ... more >>>

TR12-101 | 10th August 2012
Oded Goldreich, Shafi Goldwasser, Dana Ron

On the possibilities and limitations of pseudodeterministic algorithms

We study the possibilities and limitations
of pseudodeterministic algorithms,
a notion put forward by Gat and Goldwasser (2011).
These are probabilistic algorithms that solve search problems
such that on each input, with high probability, they output
the same solution, which may be thought of as a canonical solution.
We consider ... more >>>

TR14-178 | 5th December 2014
Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

Heuristic time hierarchies via hierarchies for sampling distributions

We give a new simple proof of the time hierarchy theorem for heuristic BPP originally proved by Fortnow and Santhanam [FS04] and then simplified and improved by Pervyshev [P07]. In the proof we use a hierarchy theorem for sampling distributions recently proved by Watson [W13]. As a byproduct we get ... more >>>

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