We give simple deterministic reductions demonstrating the NP-hardness of approximating the nearest codeword problem and minimum distance problem within arbitrary constant factors (and almost-polynomial factors assuming NP cannot be solved in quasipolynomial time). The starting point is a simple NP-hardness result without a gap, and is thus "PCP-free." Our approach ... more >>>

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 >>>