All reports by Author Yaroslav Alekseev:

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TR22-176
| 1st December 2022
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Yaroslav Alekseev, Edward Hirsch#### The power of the Binary Value Principle

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TR19-142
| 23rd October 2019
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Yaroslav Alekseev, Dima Grigoriev, Edward Hirsch, Iddo Tzameret#### Semi-Algebraic Proofs, IPS Lower Bounds and the $\tau$-Conjecture: Can a Natural Number be Negative?

Revisions: 1

Yaroslav Alekseev, Edward Hirsch

The (extended) Binary Value Principle (eBVP, the equation $\sum x_i 2^{i-1} = -k$ for $k > 0$

and in the presence of $x_i^2=x_i$) has received a lot of attention recently, several lower

bounds have been proved for it [Alekseev et al 20, Alekseev 21, Part and Tzameret 21].

Also ...
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Yaroslav Alekseev, Dima Grigoriev, Edward Hirsch, Iddo Tzameret

We introduce the `binary value principle' which is a simple subset-sum instance expressing that a natural number written in binary cannot be negative, relating it to central problems in proof and algebraic complexity. We prove conditional superpolynomial lower bounds on the Ideal Proof System (IPS) refutation size of this instance, ... more >>>