# A hitting set construction, with application to arithmetic circuit lower bounds

Abstract : A polynomial identity testing algorithm must determine whether a given input polynomial is identically equal to 0. We give a deterministic black-box identity testing algorithm for univariate polynomials of the form $\sum_{j=0}^t c_j X^{\alpha_j} (a + b X)^{\beta_j}$. From our algorithm we derive an exponential lower bound for representations of polynomials such as $\prod_{i=1}^{2^n} (X^i-1)$ under this form. It has been conjectured that these polynomials are hard to compute by general arithmetic circuits. Our result shows that the hardness from derandomization'' approach to lower bounds is feasible for a restricted class of arithmetic circuits. The proof is based on techniques from algebraic number theory, and more precisely on properties of the height function of algebraic numbers.
Keywords :
Type de document :
Pré-publication, Document de travail
14 pages. 2009
Domaine :

Littérature citée [23 références]

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00408713
Contributeur : Pascal Koiran <>
Soumis le : lundi 7 décembre 2009 - 23:01:27
Dernière modification le : mardi 24 avril 2018 - 13:52:38
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 11:17:26

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### Identifiants

• HAL Id : ensl-00408713, version 2
• ARXIV : 0907.5575

### Citation

Pascal Koiran. A hitting set construction, with application to arithmetic circuit lower bounds. 14 pages. 2009. 〈ensl-00408713v2〉

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