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Electronic Colloquium on Computational Complexity

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Reports tagged with ROABP:
TR14-085 | 29th June 2014
Manindra Agrawal, Rohit Gurjar, Arpita Korwar, Nitin Saxena

Hitting-sets for ROABP and Sum of Set-Multilinear circuits

We give a $n^{O(\log n)}$-time ($n$ is the input size) blackbox polynomial identity testing algorithm for unknown-order read-once oblivious algebraic branching programs (ROABP). The best time-complexity known for this class was $n^{O(\log^2 n)}$ due to Forbes-Saptharishi-Shpilka (STOC 2014), and that too only for multilinear ROABP. We get rid of their ... more >>>

TR16-009 | 28th January 2016
Rohit Gurjar, Arpita Korwar, Nitin Saxena

Identity Testing for constant-width, and commutative, read-once oblivious ABPs

We give improved hitting-sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known variable order. The best hitting-set known for this case had cost $(nw)^{O(\log n)}$, where $n$ is the number of variables and $w$ is the width of ... more >>>

TR20-042 | 31st March 2020
Pranav Bisht, Nitin Saxena

Poly-time blackbox identity testing for sum of log-variate constant-width ROABPs

Blackbox polynomial identity testing (PIT) affords 'extreme variable-bootstrapping' (Agrawal et al, STOC'18; PNAS'19; Guo et al, FOCS'19). This motivates us to study log-variate read-once oblivious algebraic branching programs (ROABP). We restrict width of ROABP to a constant and study the more general sum-of-ROABPs model. We give the first poly($s$)-time blackbox ... more >>>

TR21-015 | 15th February 2021
Chandan Saha, Bhargav Thankey

Hitting Sets for Orbits of Circuit Classes and Polynomial Families

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 >>>

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