Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower bounds for linear data structures would imply new bounds for rigid matrices. However, their result utilizes an algorithm that requires an $NP$ oracle, and hence, the rigid matrices are not explicit. In this work, we derive an equivalence between ... more >>>

In this paper, we study the static cell probe complexity of non-adaptive data structures that maintain a subset of $n$ points from a universe consisting of $m=n^{1+\Omega(1)}$ points. A data structure is defined to be non-adaptive when the memory locations that are chosen to be accessed during a query depend ... more >>>

The main motivation for studying linear data structures and circuits is the intuition that non-linear advice cannot help in computing a linear operator. Jukna and Schnitger formalized this as a conjecture which states that all circuits computing a linear operator can be ``linearized," with only a constant size blow-up. We ... more >>>

In this work we observe a tight connection between three topics: $NC^0$ cryptography, $NC^0$ range avoidance, and static data structure lower bounds. Using this connection, we leverage techniques from the cryptanalysis of $NC^0$ PRGs to prove state-of-the-art results in the latter two subjects. Our main result is a quadratic improvement ... more >>>

We prove an $\Omega((\log n/\log\log n)^2)$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge insertions. This improves the $\widetilde{\Omega}(\log^{3/2} n)$ lower bound of Larsen and Yu [SICOMP 2025], and matches the ... more >>>