ECCC-Report TR22-070https://eccc.weizmann.ac.il/report/2022/070Comments and Revisions published for TR22-070en-usMon, 09 May 2022 07:31:19 +0300
Paper TR22-070
| On Solving Sparse Polynomial Factorization Related Problems |
Ilya Volkovich,
Pranav Bisht
https://eccc.weizmann.ac.il/report/2022/070In a recent result of Bhargava, Saraf and Volkovich [FOCS’18; JACM’20], the first sparsity bound for constant individual degree polynomials was shown. In particular, it was shown that any factor of a polynomial with at most $s$ terms and individual degree bounded by $d$ can itself have at most $s^{O(d^2\log n)}$ terms. It is conjectured, though, that the "true" sparsity bound should be polynomial (i.e. $s^{poly(d)}$). In this paper we provide supporting evidence for this conjecture by presenting polynomial-time algorithms for several problems that would be implied by a polynomial-size sparsity bound. In particular, we give an efficient (deterministic) identity testing algorithms for $\Sigma^{[2]}\Pi\Sigma\Pi^{[\deg_{x_i} \leq d]}$ circuits and testing if a sparse polynomial is an exact power. Hence, our algorithms rely on different techniques.Mon, 09 May 2022 07:31:19 +0300https://eccc.weizmann.ac.il/report/2022/070