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

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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.

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Authors and Affiliations

  1. Faculty of Electronics and Computer Science, Aalen University, Aalen, Germany

    Rohit Gurjar & Thomas Thierauf

  2. Department of Computer Science and Engineering, IIT Kanpur, Kanpur, India

    Arpita Korwar & Nitin Saxena

Authors
  1. Rohit Gurjar
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  2. Arpita Korwar
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  3. Nitin Saxena
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  4. Thomas Thierauf
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Correspondence to Rohit Gurjar.

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Gurjar, R., Korwar, A., Saxena, N. et al. Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs. comput. complex. 26, 835–880 (2017). https://doi.org/10.1007/s00037-016-0141-z

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