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Electronic Colloquium on Computational Complexity

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TR20-041 | 29th March 2020
Mrinal Kumar, Ben Lee Volk

A Polynomial Degree Bound on Defining Equations of Non-rigid Matrices and Small Linear Circuits

Revisions: 1

We show that there is a defining equation of degree at most poly(n) for the (Zariski closure of the) set of the non-rigid matrices: that is, we show that for every large enough field $\mathbb{F}$, there is a non-zero $n^2$-variate polynomial $P \in \mathbb{F}(x_{1, 1}, \ldots, x_{n, n})$ of degree ... more >>>


TR20-040 | 25th March 2020
Andrei Krokhin, Jakub Opršal, Marcin Wrochna, Stanislav Zivny

Topology and adjunction in promise constraint satisfaction

The approximate graph colouring problem concerns colouring a $k$-colourable
graph with $c$ colours, where $c\geq k$. This problem naturally generalises
to promise graph homomorphism and further to promise constraint satisfaction
problems. Complexity analysis of all these problems is notoriously difficult.
In this paper, we introduce ... more >>>


TR20-039 | 25th March 2020
Pranjal Dutta, Nitin Saxena, Thomas Thierauf

Lower bounds on the sum of 25th-powers of univariates lead to complete derandomization of PIT

We consider the univariate polynomial $f_d:=(x+1)^d$ when represented as a sum of constant-powers of univariate polynomials. We define a natural measure for the model, the support-union, and conjecture that it is $\Omega(d)$ for $f_d$.

We show a stunning connection of the conjecture to the two main problems in algebraic ... more >>>



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