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Building above Read-once Polynomials: Identity Testing and Hardness of Representation

  • Meena Mahajan
  • B. V. Raghavendra Rao
  • Karteek Sreenivasaiah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8591)

Abstract

Polynomial Identity Testing (PIT) algorithms have focussed on polynomials computed either by small alternation-depth arithmetic circuits, or by read-restricted formulas. Read-once polynomials (ROPs) are computed by read-once formulas (ROFs) and are the simplest of read-restricted polynomials. Building structures above these, we show:
  1. 1

    A deterministic polynomial-time non-black-box PIT algorithm for ∑ (2)· ∏ ·ROF.

     
  2. 2

    Weak hardness of representation theorems for sums of powers of constant-free ROPs and for 0-justified alternation-depth-3 ROPs.

     

Keywords

Polynomial Identity Arithmetic Circuit Multilinear Polynomial Isomorphism Testing Deterministic Polynomial Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Meena Mahajan
    • 1
  • B. V. Raghavendra Rao
    • 2
  • Karteek Sreenivasaiah
    • 1
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Indian Institute of Technology MadrasChennaiIndia

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