computational complexity

, Volume 26, Issue 4, pp 835–880 | Cite as

Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs

  • Rohit Gurjar
  • Arpita Korwar
  • Nitin Saxena
  • Thomas Thierauf
Article
  • 19 Downloads

Abstract

A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching program (ABP) where each variable occurs in at most one layer. We give the first polynomial-time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial-time complexity \({n^{O({\rm log}\,n)}}\). In both the cases, our time complexity is double exponential in the number of ROABPs.

ROABPs are a generalization of set-multilinear depth-3 circuits. The prior results for the sum of constantly many set-multilinear depth-3 circuits were only slightly better than brute force, i.e., exponential time. Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration. We relate basis isolation to rank concentration and extend it to a sum of two ROABPs using evaluation dimension.

Subject classification

68Q25 68W30 

Keywords

Polynomial identity testing hitting-sets sum of ROABPs 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Rohit Gurjar
    • 1
  • Arpita Korwar
    • 2
  • Nitin Saxena
    • 2
  • Thomas Thierauf
    • 1
  1. 1.Faculty of Electronics and Computer ScienceAalen UniversityAalenGermany
  2. 2.Department of Computer Science and EngineeringIIT KanpurKanpurIndia

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