Proof complexity, the study of the lengths of proofs in
propositional logic, is an area of study that is fundamentally connected
both to major open questions of computational complexity theory and
to practical properties of automated theorem provers. In the last
decade, there have been a number of significant advances ... more >>>

We say that two given polynomials $f, g \in R[x_1, \ldots, x_n]$, over a ring $R$, are equivalent under shifts if there exists a vector $(a_1, \ldots, a_n)\in R^n$ such that $f(x_1+a_1, \ldots, x_n+a_n) = g(x_1, \ldots, x_n)$. This is a special variant of the polynomial projection problem in Algebraic ... more >>>

Guo, Saxena, and Sinhababu (TOC'18, CCC'18) defined a natural, approximative analog of the polynomial system satisfiability problem, which they called approximate polynomial satisfiability (APS). They proved algebraic and geometric properties of it and showed an NP-hardness lower bound and a PSPACE upper bound for it. They further established how the ... more >>>