Matrix powering, and more generally iterated matrix multiplication, is a fundamental linear algebraic primitive with myriad applications in computer science. Of particular interest is the problem's space complexity as it constitutes the main route towards resolving the $\mathbf{BPL}$ vs. $\mathbf{L}$ problem. The seminal work by Saks and Zhou (FOCS 1995) ... more >>>

We give a deterministic space-efficient algorithm for approximating powers of stochastic matrices. On input a $w \times w$ stochastic matrix $A$, our algorithm approximates $A^{n}$ in space $\widetilde{O}(\log n + \sqrt{\log n}\cdot \log w)$ to within high accuracy. This improves upon the seminal work by Saks and Zhou (FOCS'95), that ... more >>>

Weighted pseudorandom generators (WPRGs), introduced by Braverman, Cohen and Garg [BCG20], is a generalization of pseudorandom generators (PRGs) in which arbitrary real weights are considered rather than a probability mass. Braverman et al. constructed WPRGs against read once branching programs (ROBPs) with near-optimal dependence on the error parameter. Chattopadhyay and ... more >>>