A famous conjecture of Tuza states that the minimum number of edges needed to cover all the triangles in a graph is at most twice the maximum number of edge-disjoint triangles. This conjecture was couched in a broader setting by Aharoni and Zerbib who proposed a hypergraph version of this ... more >>>

Valiant (1980) showed that general arithmetic circuits with negation can be exponentially more powerful than monotone ones. We give the first qualitative improvement to this classical result: we construct a family of polynomials $P_n$ in $n$ variables, each of its monomials has positive coefficient, such that $P_n$ can be computed ... more >>>

In this work, we initiate the study of proximity testing to Algebraic Geometry (AG) codes. An AG code $C = C(\mathcal C, \mathcal P, D)$ is a vector space associated to evaluations on $\mathcal P$ of functions in the Riemann-Roch space $L_\mathcal C(D)$. The problem of testing proximity to an ... more >>>