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Electronic Colloquium on Computational Complexity

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Reports tagged with Decision Tree:
TR02-019 | 20th March 2002
Nader Bshouty, Lynn Burroughs

On the proper learning of axis parallel concepts

We study the proper learnability of axis parallel concept classes
in the PAC learning model and in the exact learning model with
membership and equivalence queries. These classes include union of boxes,
DNF, decision trees and multivariate polynomials.

For the {\it constant} dimensional axis parallel concepts $C$
we ... more >>>

TR02-054 | 5th September 2002
Detlef Sieling

Minimization of Decision Trees is Hard to Approximate

Decision trees are representations of discrete functions with widespread applications in, e.g., complexity theory and data mining and exploration. In these areas it is important to obtain decision trees of small size. The minimization problem for decision trees is known to be NP-hard. In this paper the problem is shown ... more >>>

TR12-163 | 24th November 2012
Avishay Tal

Properties and Applications of Boolean Function Composition

For Boolean functions $f:\{0,1\}^n \to \{0,1\}$ and $g:\{0,1\}^m \to \{0,1\}$, the function composition of $f$ and $g$ denoted by $f\circ g : \{0,1\}^{nm} \to \{0,1\}$ is the value of $f$ on $n$ inputs, each of them is the calculation of $g$ on a distinct set of $m$ Boolean variables. Motivated ... more >>>

TR13-149 | 28th October 2013
Albert Atserias, Neil Thapen

The Ordering Principle in a Fragment of Approximate Counting

The ordering principle states that every finite linear order has a least element. We show that, in the relativized setting, the surjective weak pigeonhole principle for polynomial time functions does not prove a Herbrandized version of the ordering principle over $\mathrm{T}^1_2$. This answers an open question raised in [Buss, Ko{\l}odziejczyk ... more >>>

TR16-062 | 18th April 2016
Avishay Tal

On The Sensitivity Conjecture

The sensitivity of a Boolean function $f:\{0,1\}^n \to \{0,1\}$ is the maximal number of neighbors a point in the Boolean hypercube has with different $f$-value. Roughly speaking, the block sensitivity allows to flip a set of bits (called a block) rather than just one bit, in order to change the ... more >>>

TR17-107 | 1st June 2017
Anurag Anshu, Dmytro Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal

A Composition Theorem for Randomized Query complexity

Revisions: 1

Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $\R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow \{0,1\}$, $\R_{1/3}(f\circ g^n) = \Omega(\R_{4/9}(f)\cdot\R_{1/2-1/n^4}(g))$, where $f \circ g^n$ is the relation obtained by composing $f$ and $g$. ... more >>>

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

On (Simple) Decision Tree Rank

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 >>>

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