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Electronic Colloquium on Computational Complexity

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All reports by Author Alexey Milovanov:

TR24-034 | 19th February 2024
Bruno Loff, Alexey Milovanov

The hardness of decision tree complexity

Let $f$ be a Boolean function given as either a truth table or a circuit. How difficult is it to find the decision tree complexity, also known as deterministic query complexity, of $f$ in both cases? We prove that this problem is $NC$-hard and PSPACE-hard, respectively. The second bound is ... more >>>

TR22-134 | 23rd September 2022
Greg McLellan, Alexey Milovanov

Some Games on Turing Machines and Power from Random Strings

Revisions: 1

Denote by $R$ the set of strings with high Kolmogorov complexity. In [E. Allender, H. Buhrman, M. Kouck\'y, D. van Melkebeek, and D. Ronneburger.
Power from random strings.
\emph{SIAM Journal on Computing}, 35:1467--1493, 2006.] the idea of using $R$ as an oracle for resource-bounded computation models was presented. This idea ... more >>>

TR19-035 | 5th March 2019
Alexey Milovanov

PIT for depth-4 circuits and Sylvester-Gallai theorem for polynomials

This text is a development of a preprint of Ankit Gupta.

We present an approach for devising a deterministic polynomial time whitekbox identity testing (PIT) algorithm for depth-$4$ circuits with bounded top fanin.
This approach is similar to Kayal-Saraf approach for depth-$3$ circuits. Kayal and Saraf based their ... more >>>

TR17-043 | 3rd March 2017
Alexey Milovanov, Nikolay Vereshchagin

Stochasticity in Algorithmic Statistics for Polynomial Time

A fundamental notion in Algorithmic Statistics is that of a stochastic object, i.e., an object having a simple plausible explanation. Informally, a probability distribution is a plausible explanation for $x$ if it looks likely that $x$ was drawn at random with respect to that distribution. In this paper, we ... more >>>

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