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REPORTS > KEYWORD > KRW CONJECTURE:
Reports tagged with KRW conjecture:
TR18-160 | 12th September 2018
Anna Gal, Avishay Tal, Adrian Trejo Nuñez

#### Cubic Formula Size Lower Bounds Based on Compositions with Majority

We define new functions based on the Andreev function and prove that they require $n^{3}/polylog(n)$ formula size to compute. The functions we consider are generalizations of the Andreev function using compositions with the majority function. Our arguments apply to composing a hard function with any function that agrees with the ... 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 >>>

TR20-116 | 1st August 2020
Ivan Mihajlin, Alexander Smal

#### Toward better depth lower bounds: the XOR-KRW conjecture

In this paper, we propose a new conjecture, the XOR-KRW conjecture, which is a relaxation of the Karchmer-Raz-Wigderson conjecture [KRW95]. This relaxation is still strong enough to imply $\mathbf{P} \not\subseteq \mathbf{NC}^1$ if proven. We also present a weaker version of this conjecture that might be used for breaking $n^3$ lower ... more >>>

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