Emily Yao | Searcharxiv

arXiv2026

Schmidt's Game and Vitali Sets

While many types of non-measurable sets are never $(\alpha, \beta)$-winning in the sense of Schmidt's game, we show that this is not the case for certain Vitali sets. Our main theorems show that for certain values of $\alpha, \beta$ one can construct a Vitali set which is $(\alpha, \beta)$-winning, while for other values of $\alpha,\beta$ every Vitali set is $(\alpha,\beta)$-losing. We also investigate the $(\alpha,\beta)$-Schmidt game for various other types of pathological sets, highlighting their differences from Vitali sets.

math.LO↗

arXiv2025

zkStruDul: Programming zkSNARKs with Structural Duality

Non-Interactive Zero Knowledge (NIZK) proofs, such as zkSNARKS, let one prove knowledge of private data without revealing it or interacting with a verifier. While existing tooling focuses on specifying the predicate to be proven, real-world applications optimize predicate definitions to minimize proof generation overhead, but must correspondingly transform predicate inputs. Implementing these two steps separately duplicates logic that must precisely match to avoid catastrophic security flaws. We address this shortcoming with zkStruDul, a language that unifies input transformations and predicate definitions into a single combined abstraction from which a compiler can project both procedures, eliminating duplicate code and problematic mismatches. zkStruDul provides a high-level abstraction to layer on top of existing NIZK technology and supports important features like recursive proofs. We provide a source-level semantics and prove its behavior is identical to the projected semantics, allowing straightforward standard reasoning.

cs.PL↗