


Dean
Doron, Dana Moshkovitz, Justin Oh, David Zuckerman Near Optimal Pseudorandomness From Hardness, Starting with a hard function, we construct
pseudorandom generators that use seed (1+e)logn to output n
bits that look random to sizen circuits. Existing constructions had seed clogn for a large
c>1. This allows us to derandomize any randomized algorithm with minimal
slowdown. Along the way, we beat the hybrid argument and show
a tight connection between pseudoentropy generators and locally list
recoverable codes. 
Dana Moshkovitz Sliding Scale Conjectures in PCP, We still don’t have PCP theorems where the
error is as low as we think it should be, and as a result, we can’t prove desirable
hardness of approximation results. This survey is about what we have and
where we’re stuck. SIGACT Open Problems Column 2019 [Survey] 
Dana Moshkovitz, Justin Oh, David Zuckerman Randomness Efficient Noise Stability and Generalized
Small Bias Sets, We generalize epsilon biased sets to general product
distributions and construct such with small support. This lets us define a
randomness efficient version of the noise stability test. 
Subhash Khot,
Dor Minzer, Dana Moshkovitz, Shmuel Safra Small Set Expansion in The Johnson Graph, The Johnson graph is a slice of the Boolean hypercube
(i.e., we focus only on strings of a fixed Hamming weight). In this paper we
characterize the small nonexpanding sets in this graph. The paper led to a
similar characterization for the Grassmann graph and the resolution of the Two
to Two Conjecture in PCP. 
Dana Moshkovitz, Michal Moshkovitz Entropy Samplers and Strong Generic Lower Bounds For
Space Bounded Learning, Consider the following simple (inefficient) algorithms
for learning in the PAC model [where one wishes to learn a function h from
random labelled examples (x,h(x))]: (1) minimize the number of examples by
deducing all possible conclusions from every example. (2) minimize space by
enumerating over the possible hypotheses, checking each example only against
the current hypothesis. We show that, for a wide family of possible h’s,
every algorithm that is more space efficient than (1) must use as many
examples as (2). The proceedings of the 9th Innovations in
Theoretical Computer Science conference (ITCS18) 
Dana Moshkovitz, Michal Moshkovitz Mixing Implies Lower Bounds For Space Bounded
Learning, We develop a combinatorial framework for analyzing
space bounded learning. The
proceedings of the 30th Annual Conference on Learning Theory (COLT17)

Eden
Chlamtáč, Pasin
Manurangsi, Dana Moshkovitz, Aravindan Vijayaraghavan Approximation Algorithms for Label Cover and The
LogDensity Threshold, We design and analyze stateoftheart
approximation algorithms for Label Cover (aka projection games), the problem
that is the basis of known optimal inapproximability results. The
proceedings of the 28th Annual ACMSIAM Symposium on Discrete Algorithms (SODA17) 
Subhash Khot,
Dana Moshkovitz Candidate Hard Unique Game, We propose a construction of a Boolean unique
game along with some evidence that it might be hard. Up to this work there
were no proposals for possibly hard unique games (only works ruling out
natural deterministic and randomized constructions). The
proceedings of the 48th Annual Symposium on the Theory of Computing (STOC16)
Preliminary version without analysis: ECCC TR14142
Lemma in the proof: Direct Product Testing With
Nearly Identical Sets, ECCC
TR14182 [paper] 
Ofer Grossman, Dana Moshkovitz Amplification and Derandomization Without Slowdown, We show a method for decreasing the error
probability of randomized algorithms without increasing the asymptotic
runtime via a fun puzzle that we name “the biased coin problem” (it’s about
finding a biased coin in a pile of identical coins, many of which are biased,
by making as few coin tosses as possible). We also show a method for converting randomized
algorithms to deterministic nonuniform algorithms without asymptotic
increase in the runtime. The method requires a verifier that checks the
randomized algorithm while only looking at a sketch of the input. The
proceedings of the 57th Annual IEEE
Symposium on Foundations of Computer
Science (FOCS16) 
Dana Moshkovitz, Govind Ramnarayan, Henry Yuen A NoGo Theorem for
Derandomized Parallel Repetition: Beyond FeigeKilian, Counterintuitively,
it seems that parallel repetition cannot be made randomness efficient. In 93
Feige and Kilian proved that for games with constant graph degree. This paper
shows a different obstacle that applies even for games with large
degree. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (RANDOM16) [paper] 
Gil Goldshlager,
Dana Moshkovitz Approximating kCSP
For Large Alphabet, This paper was Gil’s
undergrad project and it extends the stateoftheart approximation algorithm
for constraint satisfaction problem to large alphabet. [paper] 
Pasin Manurangsi, Dana
Moshkovitz Approximating Dense
Max 2CSPs, This paper gives
stateoftheart approximation algorithms for constraint satisfaction
problems on dense graphs. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX15)
[paper] 
Dana Moshkovitz Parallel Repetition
From Fortification, The notoriously hard
to analyze parallel repetition turns out to be easy to analyze and with
better parameters than previously thought to be possible, as long as one
makes a slight modification to the game (“fortification”) before repeating.
This paper gives possibly the simplest known analysis for transforming a
basic PCP Theorem to Label Cover form as needed for hardness of
approximation. The
proceedings of the 55th Annual IEEE Symposium on Foundations of Computer
Science (FOCS14) The latest version includes an extremely simple
proof of parallel repetition and a correction to the fortification lemma. 
Dana Moshkovitz Low Degree Test
With Polynomially Small Error, We show a low
degree test that has very low error. Making the test randomnessefficient
would prove the Sliding Scale Conjecture. [paper] Computational
Complexity journal, 2016 (Previous version “An
Approach To The Sliding Scale Conjecture Via Parallel Repetition For Low
Degree Testing”, 
Sarah Eisenstat,
Dana Moshkovitz, Robert E.
Tarjan, Siyao Xu Minimum Spanning
Tree in Deterministic Linear Time For Graphs of High Girth, Finding the minimum
spanning tree of a graph in deterministic linear time is an outstanding open
problem (there is a beautiful randomized algorithm). This paper solves it in the case of graphs
with high girth. It turned out that a previous
paper implicitly had such an algorithm too. [paper] 
Scott Aaronson, Russell Impagliazzo, Dana
Moshkovitz AM with Multiple
Merlins, We define and
explore the complexity class AM(k) in which there are k noncommunicating
provers. This paper introduced “birthday repetition” that found many uses
since, most notably, proving the intractability of computing approximate Nash
equilibrium. Computational
Complexity Conference (CCC14) 
Pasin Manurangsi, Dana
Moshkovitz Improved
Approximation Algorithms for Projection Games, We give stateoftheart
approximation algorithms for projection games (Label Cover) with perfect
completeness, which is the case relevant to hardness of approximation. ArXiv 1408.4048 (full version) The
Proceedings of the 21st European Symposium on Algorithms (ESA13) 
Vitaly Abdrashitov, Muriel Médard,
Dana Moshkovitz Matched Filter Decoding of
Random Binary and Gaussian Codes in Broadband Gaussian Channel, We show that the random binary code is essentially
as good as a Gaussian code in Gaussian channels. 
Dana Moshkovitz The Projection
Games Conjecture and the NPHardness of lnnApproximating SetCover, We show how to
deduce optimal inapproximability for SetCover under an assumption about PCP.
The assumption was proved after the publication of the paper. This paper explicitly
defined “The Projection Games Conjecture” about the hardness of approximating
projection games (aka Label Cover), and the assumption
needed for SetCover was a quantitatively weaker version of that conjecture. 
Noga Alon,
Sanjeev Arora, Rajsekar Manokaran, Dana
Moshkovitz, Omri Weinstein, Inapproximability
of Densest kSubgraph From Average Case Hardness, There’s a huge gap
between the best approximation algorithms for Densest kSubgraph (polynomial
approximation) and the best hardness results (ruling out PTAS). We rule out
constant factor approximation for the densest ksubgraph problem assuming
averagecase hardness of the planted clique problem (alternatively, assuming
averagecase hardness of kAND). [paper] 
Dana Moshkovitz, We describe a stateoftheart construction of PCP. Most
details are omitted and the focus is on the main ideas. [Survey] 
Dana Moshkovitz, The Tale of the PCP Theorem (popular article), This is an article I wrote for the students’ magazine of the
ACM. It assumes undergrad familiarity with computer science and surveys
approximation algorithms and hardness of approximation, the PCP theorem and
its proof, the Unique Games Conjecture and optimal inapproximability results. ACM XRDS
2012 [Survey] 
Subhash Khot, Dana
Moshkovitz We show that the least mean squares algorithm is optimal for
solving real linear equations, and we do so in the challenging case of
finding a solution that is far from 0 for a homogeneous system of equations.
Along the way, we develop robust real versions of linearity testing (via
Hermite analysis) and dictator testing (via rounding algorithms). Our
motivation for this paper was the vision that robust real linear equation SIAM Journal on
Computing, 42(3), 752791, 2013 ECCC
TR10112 A previous version achieving hardness under the Unique Games
Conjecture: ECCC TR10053 
Dana Moshkovitz A univariate
polynomial of degree d has at most d roots. A multivariate polynomial of
degree d over a finite field F has at most d/F fraction of roots. The
latter is known as the incredibly useful SchwartzZippel Lemma. We give a
simple proof of it by reduction to the univariate case. 
Dana Moshkovitz, Ran Raz Optimal NPhardness
of approximation results rely on a PCP Theorem of a special form (hardness of
projection games/LabelCover). In this 139page paper we prove the first such
theorem with subconstant error and almost linear size, implying a sharp
phase transition for the inapproximability of problems like Max3SAT,
Max3LIN, and many others. 
Dana Moshkovitz, Ran Raz We prove the first PCP Theorem (constant number of queries)
with both subconstant error probability and almost linear proof size. Prior
to this work there were PCP Theorems with either subconstant error
probability or almost linear size. 
Dana Moshkovitz, Ran Raz We show the first low degree test that is both
randomnessefficient and has low error probability, resolving an open problem
that stood for a few years prior. The challenge was to find a family of
affine subspaces that, on one hand, was small and pseudorandom, and, on the
other hand, was sufficiently dense in low dimensional spaces. SIAM
Journal on Computing, 38(1):140180, 2008 
Adi Akavia,
Oded Goldreich, Shafi Goldwasser, Dana
Moshkovitz We give further evidence that the hardness of one way
functions cannot be proved via reductions to NPhard problems. If it could,
the polynomial hierarchy would have collapsed to its second level. 
Noga Alon, In krestriction problems, one is given a set of tests on k
symbols, and the task is to find a small set of sizem strings such that for
every k positions, for every test, there is a string in the set that
satisfies the test in those positions. This formalism captures problems like perfect
hashing, group testing, color coding, set cover gadget, etc. We further
develop a method for solving krestriction problems via the Necklace
Splitting Theorem in algebraic topology. We also give new applications, like
an improved NPhardness of approximating SetCover. The
ACM Transactions on Algorithms, 2(2):153177, 2006 