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Published: 24/02/2017Research in the last decade has shown that to prove lower bounds or to derandomize polynomial identity testing (PIT) for general arithmetic circuits it suffices to solve these questions for restricted ... Read moreSource: weizmann.ac.il


Published: 22/02/2017In 1979 Valiant showed that the complexity class VP_e of families with polynomially bounded formula size is contained in the class VP_s of families that have algebraic branching programs (ABPs) of pol ... Read moreSource: weizmann.ac.il

Published: 19/02/2017Assume that the edges of the complete bipartite graph $K_{n,n}$ are labeled with elements of $\mathbb{F}_2^d$, such that the sum over any simple cycle is nonzero. What is the smallest possible value o ... Read moreSource: weizmann.ac.il

Published: 19/02/2017We devise a new technique to prove lower bounds for the proof size in resolutiontype calculi for quantified Boolean formulas (QBF). The new technique applies to the strong expansion system IRcalc an ... Read moreSource: weizmann.ac.il

Published: 19/02/2017The known proofs of $\text{MA}\subseteq\text{PP}$ incur a quadratic overhead in the running time. We prove that this quadratic overhead is necessary for blackbox simulations; in particular, we obtain ... Read moreSource: weizmann.ac.il

Published: 18/02/2017A Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is called a dictator if it depends on exactly one variable i.e $f(x_1, x_2, \ldots, x_n) = x_i$ for some $i\in [n]$. In this work, we study a $k$qu ... Read moreSource: weizmann.ac.il

Published: 18/02/2017Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of \emph{adaptive} testing algorithms, whe ... Read moreSource: weizmann.ac.il

Published: 17/02/2017An algebraic branching program (ABP) is a directed acyclic graph, with a start vertex $s$, and end vertex $t$ and each edge having a weight which is an affine form in $\F[x_1, x_2, \ldots, x_n]$. An A ... Read moreSource: weizmann.ac.il

Published: 17/02/2017We show a reduction from the existence of explicit tnonmalleable extractors with a small seed length, to the construction of explicit twosource extractors with small error for sources with arbitrar ... Read moreSource: weizmann.ac.il

Published: 16/02/2017A Boolean function is said to have maximal sensitivity $s$ if $s$ is the largest number of Hamming neighbors of a point which differ from it in function value. We construct a pseudorandom generator wi ... Read moreSource: weizmann.ac.il

Published: 16/02/2017We prove that the $\text{P}^{\small\text{NP}}$type query complexity (alternatively, decision list width) of any boolean function $f$ is quadratically related to the $\text{P}^{\small\text{NP}}$type ... Read moreSource: weizmann.ac.il

Published: 15/02/2017We study the power of randomized complexity classes that are given oracle access to a natural property of Razborov and Rudich (JCSS, 1997) or its special case, the Minimal Circuit Size Problem (MCSP). ... Read moreSource: weizmann.ac.il

Published: 13/02/2017This paper gives the first separation between the power of {\em formulas} and {\em circuits} of equal depth in the $\mathrm{AC}^0[\oplus]$ basis (unbounded fanin AND, OR, NOT and MOD$_2$ gates). We s ... Read moreSource: weizmann.ac.il

Published: 12/02/2017An algebraic branching program (ABP) A can be modelled as a product expression $X_1\cdot X_2\cdot \dots \cdot X_d$, where $X_1$ and $X_d$ are $1 \times w$ and $w \times 1$ matrices respectively, and e ... Read moreSource: weizmann.ac.il

Published: 12/02/2017We prove a general timespace lower bound that applies for a large class of learning problems and shows that for every problem in that class, any learning algorithm requires either a memory of quadrat ... Read moreSource: weizmann.ac.il
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