Arpita Korwar

Hitting-Sets for ROABP and Sum of Set-Multilinear Circuits

We give an

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

n^{O(\log n)}

Deterministic identity testing for sum of read-once oblivious arithmetic branching programs

-time (

Identity testing for constant-width, and commutative, read-once oblivious ABPs

n

Identity Testing for Constant-Width, and Any-Order, Read-Once Oblivious Arithmetic Branching Programs

is the input size) blackbox polynomial identity testing algorithm for unknown-order read-once oblivious arithmetic branching programs (ROABPs). The best time complexity known for blackbox polynomial identity testing (PIT) for this class was

Planarizing Gadgets for Perfect Matching Do Not Exist

n^{O(\log^2 n)}

Exact Perfect Matching in Complete Graphs

due to Forbes, Saptharishi, and Shpilka [Proceedings of the 2014 ACM Symposium on Theory of Computing, 2014, pp. 867--875]. Moreover, their result holds only when the individual degree is small, while we do not need any such assumption. With this, we match the time complexity for the unknown-order ROABP with the known-order ROABP (due to Forbes and Shpilka [Proceedings of the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013, pp. 243--252]) and also with the depth-3 set-multilinear circuits (due to Agrawal, Saha, and Saxena [Proceedings of the 2013 ACM Symposium on Theory of Computing, 2013, pp. 321--330]). Our proof is simpler and involves a new technique called basis isolation. The depth-3 ...

Planarizing gadgets for perfect matching do not exist

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

Deterministic Identity Testing for Sum of Read Once ABPs.

{n^{O({\rm log}\,n)}}