Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > ORBITS:
Reports tagged with Orbits:
TR21-015 | 15th February 2021
Chandan Saha, Bhargav Thankey

#### Hitting Sets for Orbits of Circuit Classes and Polynomial Families

Revisions: 2

The orbit of an $n$-variate polynomial $f(\mathbf{x})$ over a field $\mathbb{F}$ is the set $\mathrm{orb}(f) := \{f(A\mathbf{x}+\mathbf{b}) : A \in \mathrm{GL}(n,\mathbb{F}) \ \mathrm{and} \ \mathbf{b} \in \mathbb{F}^n\}$. This paper studies explicit hitting sets for the orbits of polynomials computable by certain well-studied circuit classes. This version of the hitting set ... more >>>

TR21-062 | 29th April 2021
Vishwas Bhargava, Sumanta Ghosh

#### Improved Hitting Set for Orbit of ROABPs

Revisions: 2

The orbit of an $n$-variate polynomial $f(\mathbf{x})$ over a field $\mathbb{F}$ is the set $\{f(A \mathbf{x} + b)\,\mid\, A\in \mathrm{GL}({n,\mathbb{F}})\mbox{ and }\mathbf{b} \in \mathbb{F}^n\}$, and the orbit of a polynomial class is the union of orbits of all the polynomials in it. In this paper, we give improved constructions of ... more >>>

TR22-099 | 14th July 2022
Nikhil Gupta, Chandan Saha, Bhargav Thankey

#### Equivalence Test for Read-Once Arithmetic Formulas

We study the polynomial equivalence problem for orbits of read-once arithmetic formulas (ROFs). Read-once formulas have received considerable attention in both algebraic and Boolean complexity and have served as a testbed for developing effective tools and techniques for analyzing circuits. Two $n$-variate polynomials $f, g \in \mathbb{F}[\mathbf{x}]$ are equivalent, denoted ... more >>>

ISSN 1433-8092 | Imprint