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

__
TR06-154
| 13th December 2006
__

Joshua Buresh-Oppenheim, Valentine Kabanets, Rahul Santhanam#### Uniform Hardness Amplification in NP via Monotone Codes

__
TR06-003
| 8th January 2006
__

Joshua Buresh-Oppenheim, Rahul Santhanam#### Making Hard Problems Harder

__
TR03-084
| 27th November 2003
__

Joshua Buresh-Oppenheim, Tsuyoshi Morioka#### Relativized NP Search Problems and Propositional Proof Systems

__
TR01-074
| 12th October 2001
__

Joshua Buresh-Oppenheim, David Mitchell#### Linear and Negative Resolution are Weaker than Resolution

Comments: 1

Michael Alekhnovich, Allan Borodin, Joshua Buresh-Oppenheim, Russell Impagliazzo, Avner Magen

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 >>>

Joshua Buresh-Oppenheim, Valentine Kabanets, Rahul Santhanam

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 >>>

Joshua Buresh-Oppenheim, Rahul Santhanam

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 >>>

Joshua Buresh-Oppenheim, Tsuyoshi Morioka

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 >>>

Joshua Buresh-Oppenheim, David Mitchell

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 >>>