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Electronic Colloquium on Computational Complexity

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All reports by Author Joshua Buresh-Oppenheim:

TR09-038 | 14th April 2009
Michael Alekhnovich, Allan Borodin, Joshua Buresh-Oppenheim, Russell Impagliazzo, Avner Magen

Toward a Model for Backtracking and Dynamic Programming

We propose a model called priority branching trees (pBT ) for backtracking and dynamic
programming algorithms. Our model generalizes both the priority model of Borodin, Nielson
and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence
spans a wide spectrum of algorithms. After witnessing the ... more >>>

TR06-154 | 13th December 2006
Joshua Buresh-Oppenheim, Valentine Kabanets, Rahul Santhanam

Uniform Hardness Amplification in NP via Monotone Codes

We consider the problem of amplifying uniform average-case hardness
of languages in $\NP$, where hardness is with respect to $\BPP$
algorithms. We introduce the notion of \emph{monotone}
error-correcting codes, and show that hardness amplification for
$\NP$ is essentially equivalent to constructing efficiently
\emph{locally} encodable and \emph{locally} list-decodable monotone
codes. The ... more >>>

TR06-003 | 8th January 2006
Joshua Buresh-Oppenheim, Rahul Santhanam

Making Hard Problems Harder

We consider a general approach to the hoary problem of (im)proving circuit lower bounds. We define notions of hardness condensing and hardness extraction, in analogy to the corresponding notions from the computational theory of randomness. A hardness condenser is a procedure that takes in a Boolean function as input, as ... more >>>

TR03-084 | 27th November 2003
Joshua Buresh-Oppenheim, Tsuyoshi Morioka

Relativized NP Search Problems and Propositional Proof Systems

We consider Total Functional $\NP$ ($\TFNP$) search problems. Such problems are based on combinatorial principles that guarantee, through locally checkable conditions, that a solution to the problem exists in an exponentially-large domain, and have the property that any solution has a polynomial-size witness that can be verified in polynomial time. ... more >>>

TR01-074 | 12th October 2001
Joshua Buresh-Oppenheim, David Mitchell

Linear and Negative Resolution are Weaker than Resolution

Comments: 1

We prove exponential separations between the sizes of
particular refutations in negative, respectively linear, resolution and
general resolution. Only a superpolynomial separation between negative
and general resolution was previously known. Our examples show that there
is no strong relationship between the size and width of refutations in
negative and ... more >>>

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