Neeraj Kayal, Shubhangi Saraf

We study depth three arithmetic circuits with bounded top fanin. We give the first deterministic polynomial time blackbox identity test for depth three circuits with bounded top fanin over the field of rational numbers, thus resolving a question posed by Klivans and Spielman (STOC 2001).

Our main technical result is ... more >>>

Nitin Saxena, C. Seshadhri

Let C be a depth-3 circuit with n variables, degree d and top fanin k (called sps(k,d,n) circuits) over base field F.

It is a major open problem to design a deterministic polynomial time blackbox algorithm

that tests if C is identically zero.

Klivans & Spielman (STOC 2001) observed ...
more >>>

Malte Beecken, Johannes Mittmann, Nitin Saxena

Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials $\{f_1,\ldots, f_m\} \subset \mathbb{F}[x_1,\ldots, x_n]$ are called algebraically independent if there is no non-zero polynomial $F$ such that $F(f_1, \ldots, f_m) = 0$. The transcendence degree, $\mbox{trdeg}\{f_1,\ldots, f_m\}$, is the maximal ... more >>>

Pranav Bisht, Nitin Saxena

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 >>>