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REPORTS > KEYWORD > KRW COMPOSITION CONJECTURE:
Reports tagged with KRW composition conjecture:
TR16-035 | 11th March 2016
Irit Dinur, Or Meir

Toward the KRW Composition Conjecture: Cubic Formula Lower Bounds via Communication Complexity

Revisions: 2

One of the major challenges of the research in circuit complexity is proving super-polynomial lower bounds for de-Morgan formulas. Karchmer, Raz, and Wigderson suggested to approach this problem by proving that formula complexity behaves "as expected'' with respect to the composition of functions $f\circ g$. They showed that this conjecture, ... more >>>


TR17-146 | 1st October 2017
Or Meir

On Derandomized Composition of Boolean Functions

Revisions: 4

The composition of two Boolean functions $f:\left\{0,1\right\}^{m}\to\left\{0,1\right\}$, $g:\left\{0,1\right\}^{n}\to\left\{0,1\right\}$
is the function $f \diamond g$ that takes as inputs $m$ strings $x_{1},\ldots,x_{m}\in\left\{0,1\right\}^{n}$
and computes
\[
(f \diamond g)(x_{1},\ldots,x_{m})=f\left(g(x_{1}),\ldots,g(x_{m})\right).
\]
This operation has been used several times for amplifying different
hardness measures of $f$ and $g$. This comes at a cost: the ... more >>>


TR17-148 | 6th October 2017
Or Meir, Avishay Tal

The Choice and Agreement Problems of a Random Function

Revisions: 3

The direct-sum question is a classical question that asks whether
performing a task on $m$ independent inputs is $m$ times harder
than performing it on a single input. In order to study this question,
Beimel et. al (Computational Complexity 23(1), 2014) introduced the following related problems:

* The choice ... more >>>


TR19-120 | 11th September 2019
Or Meir

Toward Better Depth Lower Bounds: Two Results on the Multiplexor Relation

Revisions: 1

One of the major open problems in complexity theory is proving super-logarithmic
lower bounds on the depth of circuits (i.e., $\mathbf{P}\not\subseteq\mathbf{NC}^1$). Karchmer, Raz, and Wigderson (Computational Complexity 5, 3/4) suggested to approach this problem by proving that depth complexity behaves "as expected" with respect to the composition of functions $f ... more >>>


TR20-099 | 6th July 2020
Susanna de Rezende, Or Meir, Jakob Nordström, Toniann Pitassi, Robert Robere

KRW Composition Theorems via Lifting

One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., $\mathbf{P}\not\subseteq\mathbf{NC}^1$). Karchmer, Raz, and Wigderson (Computational Complexity 5(3/4), 1995) suggested to approach this problem by proving that depth complexity behaves “as expected” with respect to the composition of functions $f ... more >>>




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