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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > BOOLEAN FUNCTION COMPLEXITY:
Reports tagged with boolean function complexity:
TR06-049 | 9th April 2006
Guy Wolfovitz

The Complexity of Depth-3 Circuits Computing Symmetric Boolean Functions

Comments: 1

We give tight lower bounds for the size of depth-3 circuits with limited bottom fanin computing symmetric Boolean functions. We show that any depth-3 circuit with bottom fanin $k$ which computes the Boolean function $EXACT_{n/(k+1)}^{n}$, has at least $(1+1/k)^{n+\O(\log n)}$ gates. We show that this lower bound is tight, by ... more >>>


TR13-051 | 2nd April 2013
Eric Blais, Li-Yang Tan

Approximating Boolean functions with depth-2 circuits

We study the complexity of approximating Boolean functions with DNFs and other depth-2 circuits, exploring two main directions: universal bounds on the approximability of all Boolean functions, and the approximability of the parity function.
In the first direction, our main positive results are the first non-trivial universal upper bounds on ... more >>>


TR22-001 | 28th December 2021
Yogesh Dahiya, Meena Mahajan

On (Simple) Decision Tree Rank

Revisions: 1

In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to several non-computational complexity measures of functions such as certificate complexity. The size measure ... more >>>


TR22-143 | 7th November 2022
Sourav Chakraborty, Anna Gal, Sophie Laplante, Rajat Mittal, Anupa Sunny

Certificate games

Revisions: 1

We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output some index $i$ such that $x_i\neq y_i$, in a zero-communication setting.

We give upper and lower ... more >>>


TR24-103 | 11th June 2024
Farzan Byramji, Vatsal Jha, Chandrima Kayal, Rajat Mittal

Relations between monotone complexity measures based on decision tree complexity

In a recent result, Knop, Lovett, McGuire and Yuan (STOC 2021) proved the log-rank conjecture for communication complexity, up to $\log n$ factor, for any Boolean function composed with $AND$ function as the inner gadget. One of the main tools in this result was the relationship between monotone analogues of ... more >>>




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