Factorization of Polynomials Given By Arithmetic Branching Programs

Authors Amit Sinhababu, Thomas Thierauf

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Amit Sinhababu
  • Aalen University, Germany
Thomas Thierauf
  • Aalen University, Germany


We thank Nitin Saxena, Pranjal Dutta, Arpita Korwar, Sumanta Ghosh, Zeyu Guo and Mrinal Kumar for helpful discussions. A.S would like to thank the Institute of Theoretical Computer Science at Ulm University for the hospitality.

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Amit Sinhababu and Thomas Thierauf. Factorization of Polynomials Given By Arithmetic Branching Programs. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Given a multivariate polynomial computed by an arithmetic branching program (ABP) of size s, we show that all its factors can be computed by arithmetic branching programs of size poly(s). Kaltofen gave a similar result for polynomials computed by arithmetic circuits. The previously known best upper bound for ABP-factors was poly(s^(log s)).

Subject Classification

ACM Subject Classification
  • Theory of computation → Algebraic complexity theory
  • Arithmetic Branching Program
  • Multivariate Polynomial Factorization
  • Hensel Lifting
  • Newton Iteration
  • Hardness vs Randomness


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