Abstract
Read-k oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ABP). In this work, we give an exponential lower bound of exp(n/kO(k) ) on the width of any read-k oblivious ABP computing some explicit multilinear polynomial f that is computed by a polynomial-size depth-3 circuit. We also study the polynomial identity testing (PIT) problem for this model and obtain a white-box subexponential-Time PIT algorithm. The algorithm runs in time 2 O (n1-1/2k-1 ) and needs white box access only to know the order in which the variables appear in the ABP.
Original language | English |
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Article number | 3 |
Journal | ACM Transactions on Computation Theory |
Volume | 10 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2018 |
Keywords
- Algebraic circuits
- Algebraic complexity theory
- Lower bounds
- Polynomial identity testing
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computational Theory and Mathematics