All reports by Author Antonina Kolokolova:

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TR21-095
| 8th July 2021
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Marco Carmosino, Valentine Kabanets, Antonina Kolokolova, Igor Oliveira#### LEARN-Uniform Circuit Lower Bounds and Provability in Bounded Arithmetic

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TR19-018
| 18th February 2019
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Alexander Golovnev, Rahul Ilango, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Avishay Tal#### AC0[p] Lower Bounds against MCSP via the Coin Problem

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TR17-151
| 8th October 2017
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Paul Beame, Noah Fleming, Russell Impagliazzo, Antonina Kolokolova, Denis Pankratov, Toniann Pitassi, Robert Robere#### Stabbing Planes

Revisions: 1

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TR17-109
| 22nd June 2017
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Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Pierre McKenzie, Shadab Romani#### Does Looking Inside a Circuit Help?

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TR16-144
| 15th September 2016
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Sam Buss, Valentine Kabanets, Antonina Kolokolova, Michal Koucky#### Expander Construction in VNC${}^1$

Revisions: 2

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TR16-008
| 26th January 2016
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Marco Carmosino, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova#### Algorithms from Natural Lower Bounds

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TR13-057
| 5th April 2013
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Ruiwen Chen, Valentine Kabanets, Antonina Kolokolova, Ronen Shaltiel, David Zuckerman#### Mining Circuit Lower Bound Proofs for Meta-Algorithms

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TR13-024
| 7th February 2013
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Valentine Kabanets, Antonina Kolokolova#### Compression of Boolean Functions

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TR01-024
| 1st March 2001
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Stephen Cook, Antonina Kolokolova#### A second-order system for polynomial-time reasoning based on Graedel's theorem

Marco Carmosino, Valentine Kabanets, Antonina Kolokolova, Igor Oliveira

We investigate randomized LEARN-uniformity, which captures the power of randomness and equivalence queries (EQ) in the construction of Boolean circuits for an explicit problem. This is an intermediate notion between P-uniformity and non-uniformity motivated by connections to learning, complexity, and logic. Building on a number of techniques, we establish the ... more >>>

Alexander Golovnev, Rahul Ilango, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Avishay Tal

Minimum Circuit Size Problem (MCSP) asks to decide if a given truth table of an $n$-variate boolean function has circuit complexity less than a given parameter $s$. We prove that MCSP is hard for constant-depth circuits with mod $p$ gates, for any prime $p\geq 2$ (the circuit class $AC^0[p])$. Namely, ... more >>>

Paul Beame, Noah Fleming, Russell Impagliazzo, Antonina Kolokolova, Denis Pankratov, Toniann Pitassi, Robert Robere

We introduce and develop a new semi-algebraic proof system, called Stabbing Planes that is in the style of DPLL-based modern SAT solvers. As with DPLL, there is only one rule: the current polytope can be subdivided by

branching on an inequality and its "integer negation.'' That is, we can (nondeterministically ...
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Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova, Pierre McKenzie, Shadab Romani

The Black-Box Hypothesis, introduced by Barak et al. (JACM, 2012), states that any property of boolean functions decided efficiently (e.g., in BPP) with inputs represented by circuits can also be decided efficiently in the black-box setting, where an algorithm is given an oracle access to the input function and an ... more >>>

Sam Buss, Valentine Kabanets, Antonina Kolokolova, Michal Koucky

We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [Annals of Mathematics, 2002], and show that this analysis can be formalized in the bounded-arithmetic system $VNC^1$ (corresponding to the ``$NC^1$ reasoning''). As a corollary, we prove the ... more >>>

Marco Carmosino, Russell Impagliazzo, Valentine Kabanets, Antonina Kolokolova

Circuit analysis algorithms such as learning, SAT, minimum circuit size, and compression imply circuit lower bounds. We show a generic implication in the opposite direction: natural properties (in the sense of Razborov and Rudich) imply randomized learning and compression algorithms. This is the first such implication outside of the derandomization ... more >>>

Ruiwen Chen, Valentine Kabanets, Antonina Kolokolova, Ronen Shaltiel, David Zuckerman

We show that circuit lower bound proofs based on the method of random restrictions yield non-trivial compression algorithms for ``easy'' Boolean functions from the corresponding circuit classes. The compression problem is defined as follows: given the truth table of an $n$-variate Boolean function $f$ computable by some unknown small circuit ... more >>>

Valentine Kabanets, Antonina Kolokolova

We consider the problem of compression for ``easy'' Boolean functions: given the truth table of an $n$-variate Boolean function $f$ computable by some \emph{unknown small circuit} from a \emph{known class} of circuits, find in deterministic time $\poly(2^n)$ a circuit $C$ (no restriction on the type of $C$) computing $f$ so ... more >>>

Stephen Cook, Antonina Kolokolova

We introduce a second-order system V_1-Horn of bounded arithmetic

formalizing polynomial-time reasoning, based on Graedel's

second-order Horn characterization of P. Our system has

comprehension over P predicates (defined by Graedel's second-order

Horn formulas), and only finitely many function symbols. Other

systems of polynomial-time reasoning either ...
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