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Electronic Colloquium on Computational Complexity

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Reports tagged with Probabilistic degree:
TR19-138 | 6th October 2019
Srikanth Srinivasan, Utkarsh Tripathi, S Venkitesh

On the Probabilistic Degrees of Symmetric Boolean functions

The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high probability. Introduced by Razborov (1987), upper and lower bounds on probabilistic degrees ... more >>>

TR20-046 | 13th April 2020
Srikanth Srinivasan

A Robust Version of Heged\H{u}s's Lemma, with Applications

Heged\H{u}s's lemma is the following combinatorial statement regarding polynomials over finite fields. Over a field $\mathbb{F}$ of characteristic $p > 0$ and for $q$ a power of $p$, the lemma says that any multilinear polynomial $P\in \mathbb{F}[x_1,\ldots,x_n]$ of degree less than $q$ that vanishes at all points in $\{0,1\}^n$ of ... more >>>

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