In this work, we establish separation theorems for several subsystems of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi (J. ACM, 2018). Separation theorems are well-studied in the context of classical complexity theory, Boolean circuit complexity, and algebraic complexity.

In an important work ... more >>>

We investigate the closure properties of read-once oblivious Algebraic Branching Programs (roABPs) under various natural algebraic operations and prove the following.
- Non-closure under factoring: There is a sequence of explicit polynomials $(f_n(x_1,\ldots, x_n))_n$ that have poly(n)-sized roABPs such that some irreducible factor of $f_n$ does not have roABPs ... more >>>