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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > DANA MOSHKOVITZ:
All reports by Author Dana Moshkovitz:

TR18-078 | 23rd April 2018
Subhash Khot, Dor Minzer, Dana Moshkovitz, Muli Safra

Small Set Expansion in The Johnson Graph

This paper studies expansion properties of the (generalized) Johnson Graph. For natural numbers
t < l < k, the nodes of the graph are sets of size l in a universe of size k. Two sets are connected if
their intersection is of size t. The Johnson graph arises often ... more >>>


TR17-116 | 5th July 2017
Michal Moshkovitz, Dana Moshkovitz

Mixing Implies Strong Lower Bounds for Space Bounded Learning

With any hypothesis class one can associate a bipartite graph whose vertices are the hypotheses H on one side and all possible labeled examples X on the other side, and an hypothesis is connected to all the labeled examples that are consistent with it. We call this graph the hypotheses ... more >>>


TR17-017 | 5th February 2017
Michal Moshkovitz, Dana Moshkovitz

Mixing Implies Lower Bounds for Space Bounded Learning

One can learn any hypothesis class $H$ with $O(\log|H|)$ labeled examples. Alas, learning with so few examples requires saving the examples in memory, and this requires $|X|^{O(\log|H|)}$ memory states, where $X$ is the set of all labeled examples. A question that arises is how many labeled examples are needed in ... more >>>


TR15-158 | 27th September 2015
Ofer Grossman, Dana Moshkovitz

Amplification and Derandomization Without Slowdown

We present techniques for decreasing the error probability of randomized algorithms and for converting randomized algorithms to deterministic (non-uniform) algorithms. Unlike most existing techniques that involve repetition of the randomized algorithm, and hence a slowdown, our techniques produce algorithms with a similar run-time to the original randomized algorithms.

The ... more >>>


TR14-182 | 22nd December 2014
Dana Moshkovitz

Direct Product Testing With Nearly Identical Sets

Comments: 1

In this work we analyze a direct product test in which each of two provers receives a subset of size n of a ground set U,
and the two subsets intersect in about (1-\delta)n elements.
We show that if each of the provers provides labels to the n ... more >>>


TR14-142 | 1st November 2014
Subhash Khot, Dana Moshkovitz

Candidate Lasserre Integrality Gap For Unique Games

We propose a candidate Lasserre integrality gap construction for the Unique Games problem.
Our construction is based on a suggestion in [KM STOC'11] wherein the authors study the complexity of approximately solving a system of linear equations over reals and suggest it as an avenue towards a (positive) resolution ... more >>>


TR14-054 | 16th April 2014
Dana Moshkovitz

Parallel Repetition of Fortified Games

Revisions: 2

The Parallel Repetition Theorem upper-bounds the value of a repeated (tensored) two prover game G^k in terms of the value of the game G and the number of repetitions k.
Contrary to what one might have guessed, the value of G^k is not val(G)^k, but rather a more complicated ... more >>>


TR14-030 | 5th March 2014
Dana Moshkovitz

An Approach To The Sliding Scale Conjecture Via Parallel Repetition For Low Degree Testing

The Sliding Scale Conjecture in PCP states that there are PCP verifiers with a constant number of queries and soundness error that is exponentially small in the randomness of the verifier and the length of the prover's answers.

The Sliding Scale Conjecture is one of the oldest open problems in ... more >>>


TR14-012 | 27th January 2014
Scott Aaronson, Russell Impagliazzo, Dana Moshkovitz

AM with Multiple Merlins

Revisions: 1

We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from Arthur. One motivation for this model (which we explore in detail) comes from the close ... more >>>


TR11-112 | 10th August 2011
Dana Moshkovitz

The Projection Games Conjecture and The NP-Hardness of ln n-Approximating Set-Cover

In this paper we put forward a conjecture: an instantiation of the Sliding Scale Conjecture of Bellare, Goldwasser, Lund and Russell to projection games. We refer to this conjecture as the Projection Games Conjecture.

We further suggest the research agenda of establishing new hardness of approximation results based on the ... more >>>


TR10-112 | 15th July 2010
Subhash Khot, Dana Moshkovitz

NP-Hardness of Approximately Solving Linear Equations Over Reals

In this paper, we consider the problem of approximately solving a system of homogeneous linear equations over reals, where each
equation contains at most three variables.

Since the all-zero assignment always satisfies all the equations exactly, we restrict the assignments to be ``non-trivial". Here is
an informal statement of our ... more >>>


TR10-096 | 16th June 2010
Dana Moshkovitz

An Alternative Proof of The Schwartz-Zippel Lemma

Revisions: 1

We show a non-inductive proof of the Schwartz-Zippel lemma. The lemma bounds the number of zeros of a multivariate low degree polynomial over a finite field.

more >>>

TR10-053 | 28th March 2010
Dana Moshkovitz, Subhash Khot

Hardness of Approximately Solving Linear Equations Over Reals

Comments: 1

In this paper, we consider the problem of approximately solving a
system of homogeneous linear equations over reals, where each
equation contains at most three variables.

Since the all-zero assignment always satisfies all the equations
exactly, we restrict the assignments to be ``non-trivial". Here is
an informal statement of our ... more >>>


TR08-071 | 6th August 2008
Dana Moshkovitz, Ran Raz

Two Query PCP with Sub-Constant Error

We show that the NP-Complete language 3Sat has a PCP
verifier that makes two queries to a proof of almost-linear size
and achieves sub-constant probability of error $o(1)$. The
verifier performs only projection tests, meaning that the answer
to the first query determines at most one accepting answer to the
more >>>


TR07-026 | 21st November 2006
Dana Moshkovitz, Ran Raz

Sub-Constant Error Probabilistically Checkable Proof of Almost Linear Size

We show a construction of a PCP with both sub-constant error and
almost-linear size. Specifically, for some constant alpha in (0,1),
we construct a PCP verifier for checking satisfiability of
Boolean formulas that on input of size n uses log n + O((log
n)^{1-alpha}) random bits to query a constant ... more >>>


TR05-086 | 14th August 2005
Dana Moshkovitz, Ran Raz

Sub-Constant Error Low Degree Test of Almost Linear Size

Revisions: 1

Given a function f:F^m \rightarrow F over a finite
field F, a low degree tester tests its proximity to
an m-variate polynomial of total degree at most d
over F. The tester is usually given access to an oracle
A providing the supposed restrictions of f to
affine subspaces of ... more >>>




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