This paper demonstrates a duality between the non-robustness of polynomial time dimension and the existence of one-way functions. Polynomial-time dimension (denoted $\mathrm{cdim}_\mathrm{P}$) quantifies the density of information of infinite sequences using polynomial time betting algorithms called $s$-gales. An alternate quantification of the notion of polynomial time density of information is ... more >>>

We study weighted pseudorandom generators (WPRGs) and derandomizations for read-once branching programs (ROBPs), which are key problems towards answering the fundamental open question $\mathbf{BPL} ?{=} \mathbf{L}$.
Denote $n$ and $w$ as the length and the width of a ROBP.
We have the following results.

For standard ROBPs, there exists an ... more >>>

Relaxations for the constraint satisfaction problem (CSP) include bounded width (BW), linear program (LP), semidefinite program (SDP), affine integer program (AIP), and their combinations. Tightening relaxations systematically leads to hierarchies and stronger algorithms. For LP+AIP and SDP+AIP hierarchies, various lower bounds were shown by Ciardo and Živný (STOC 2023, STOC ... more >>>