**Rohit Gurjar, Arpita Korwar, Nitin Saxena, Thomas Thierauf**

**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(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
(or partial derivatives).